Deck 9: Hypothesis Testing

Question 1

Solve the problem.

-A researcher claims that 58% of voters favor gun control. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

A)There is not sufficient sample evidence to support the claim that 58% of voters favor gun control.
B)There is sufficient sample evidence to support the claim that more than 58% of voters favor gun control.
C)There is not sufficient sample evidence to warrant rejection of the claim that 58% of voters favor gun control.
D)There is sufficient sample evidence to warrant rejection of the claim that 58% of voters favor gun control.

Answer 1

There is not sufficient sample evidence to warrant rejection of the claim that 58% of voters favor gun control.

Question 2

Solve the problem.

-The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a mean temperature of 48°F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the mean temperature of the refrigerators is different from 48°F. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

A)There is sufficient sample evidence to support the claim that the mean temperature of the refrigerators is equal to 48°F.
B)There is not sufficient sample evidence to support the claim that the mean temperature of the refrigerators is different from 48°F.
C)There is sufficient sample evidence to support the claim that the mean temperature of the refrigerators is different from 48°F.
D)There is not sufficient sample evidence to support the claim that the mean temperature of the refrigerators is equal to 48°F.

Answer 2

There is sufficient sample evidence to support the claim that the mean temperature of the refrigerators is different from 48°F.

Question 3

Answer the question.

-A study of a brand of "in the shell" peanuts sold at sports events gives the following results: $$\begin{array} { l | l } \text { Number of } & \\\text { Peanuts per bag}& \text { balprobability } \\\hline 25 & 0.003 \\30 & 0.02 \\35 & 0.09 \\40 & 0.15 \\45 & 0.35 \\50 & 0.217 \\55 & 0.07\end{array}$$ A fan purchased a bag with 30 peanuts. What is the P-value for this result?

A)0.09
B)0.2
C)0.9
D)0.02

Answer 3

0.02

Question 4

Formulate the null and alternative hypotheses for a hypothesis test.


-The owner of a football team claims that the mean attendance at games is greater than 75,100.

A) $\mathrm { H } _ { 0 } : \mu < 75,100$
$\mathrm { H } _ { \mathrm { a } } : \mu = 75,100$

B) $\mathrm { H } _ { 0 } : \mu > 75,100$
$\mathrm { H } _ { \mathrm { a } } : \mu = 75,100$

C) $\mathrm { H } _ { 0 } : \mu = 75,100$
$\mathrm { H } _ { \mathrm { a } } : \mu > 75,100$

D) $\mathrm { H } _ { 0 } : \mu = 75,100$
$\mathrm { H } _ { \mathrm { a } } : \mu < 75,100$

Question 5

Formulate the null and alternative hypotheses for a hypothesis test.


-An entomologist writes an article in a scientific journal which claims that less than 5 in ten thousand male fireflies are unable to produce light due to a genetic mutation.

A) $\mathrm { H } _ { 0 } : \mathrm { p } > 0.0005$
$\mathrm { H } _ { \mathrm { a } } : \mathrm { p } = 0.0005$

B) $\mathrm { H } _ { 0 } : \mathrm { p } < 0.0005$
$\mathrm { H } _ { \mathrm { a } } : \mathrm { p } = 0.0005$

C) $\mathrm { H } _ { 0 } : \mathrm { p } = 0.0005$
$\mathrm { H } _ { \mathrm { a } } : \mathrm { p } < 0.0005$

D) $\mathrm { H } _ { 0 } : \mathrm { p } = 0.0005$
$\mathrm { H } _ { \mathrm { a } } : \mathrm { p } > 0.0005$

Question 6

Solve the problem.

-Carter Motor Company claims that its new sedan, the Libra, will average better than 30 miles per gallon in the city. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null
Hypothesis, state the conclusion in nontechnical terms.

A)There is not sufficient sample evidence to support the claim that the mean is less than 30 miles per gallon.
B)There is not sufficient sample evidence to support the claim that the mean is greater than 30 miles per gallon.
C)There is sufficient sample evidence to support the claim that the mean is less than 30 miles per gallon.
D)There is sufficient sample evidence to support the claim that the mean is greater than 30 miles per gallon.

Question 7

Solve the problem.

-An entomologist writes an article in a scientific journal which claims that fewer than 20 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

A)There is not sufficient sample evidence to support the claim that the proportion is greater than 20 in ten thousand.
B)There is sufficient sample evidence to support the claim that the proportion is less than 20 in ten thousand.
C)There is sufficient sample evidence to support the claim that the proportion is greater than 20 in ten thousand.
D)There is not sufficient sample evidence to support the claim that the proportion is less than 20 in ten thousand.

Question 8

In 1990, the average duration of long-distance telephone calls originating in one town was 8.5 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 8.5 minutes.

A) $\mathrm { H } _ { 0 } : \mu \neq 8.5$ minutes
$\mathrm { H } _ { \mathrm { a } } : \mu = 8.5$ minutes

B) $\mathrm { H } _ { 0 } : \mu = 8.5$ minutes
$\mathrm { H } _ { \mathrm { a } } : \mu > 8.5$ minutes

C) $\mathrm { H } _ { 0 } : \mu = 8.5$ minutes
$\mathrm { H } _ { \mathrm { a } } : \mu \neq 8.5$ minutes

D) $\mathrm { H } _ { 0 } : \mu = 8.5$ minutes
$\mathrm { H } _ { \mathrm { a } } : \mu < 8.5$ minutes

Question 9

A consumer advocacy group claims that the mean amount of juice in a 18 ounce bottled drink is not 18 ounces, as stated by the bottler.

A) $\mathrm { H } _ { 0 } : \mu = 18$ ounces
$\mathrm { H } _ { \mathrm { a } } : \mu < 18$ ounces

B) $\mathrm { H } _ { 0 } : \mu = 18$ ounces
$\mathrm { H } _ { \mathrm { a } } : \mu \neq 18$ ounces

C) $\mathrm { H } _ { 0 } : \mu = 18$ ounces
$\mathrm { H } _ { \mathrm { a } } : \mu > 18$ ounces

D) $\mathrm { H } _ { 0 } : \mu \neq 18$ ounces
$\mathrm { H } _ { \mathrm { a } } : \mu = 18$ ounces

Question 10

Solve the problem.

-A psychologist claims that more than 64 percent of the population suffers from professional problems due to extreme shyness. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

A)There is not sufficient sample evidence to support the claim that the proportion is less than 64 percent.
B)There is sufficient sample evidence to support the claim that the proportion is less than 64 percent.
C)There is not sufficient sample evidence to support the claim that the proportion is greater than 64 percent.
D)There is sufficient sample evidence to support the claim that the proportion is greater than 64 percent.

Question 11

Formulate the null and alternative hypotheses for a hypothesis test.


-A car company claims that its new sedan will have a mean gas mileage greater than 28 miles per gallon in the city.

A) $\mathrm { H } _ { 0 } : \mu > 28 \mathrm { mpg }$
$\mathrm { H } _ { \mathrm { a } } : \mu = 28 \mathrm { mpg }$

B) $\mathrm { H } _ { 0 } : \mu < 28 \mathrm { mpg }$
$\mathrm { H } _ { \mathrm { a } } : \mu = 28 \mathrm { mpg }$

C) $\mathrm { H } _ { 0 } : \mu = 28 \mathrm { mpg }$
$\mathrm { H } _ { \mathrm { a } } : \mu < 28 \mathrm { mpg }$

D) $\mathrm { H } _ { 0 } : \mu = 28 \mathrm { mpg }$
$\mathrm { H } _ { \mathrm { a } } : \mu > 28 \mathrm { mpg }$

Question 12

A manufacturer wishes to test the claim that one of its pancake mixes has a mean weight that does not equal 16 ounces as advertised.

A) $\mathrm { H } _ { 0 } : \mu = 16$ ounces
$\mathrm { H } _ { \mathrm { a } } : \mu > 16$ ounces

B) $H _ { 0 } : \mu = 16$ ounces
$\mathrm { H } _ { \mathrm { a } } : \mu < 16$ ounces

C) $\mathrm { H } _ { 0 } : \mu = 16$ ounces
$\mathrm { H } _ { \mathrm { a } } : \mu \neq 16$ ounces

D) $\mathrm { H } _ { 0 } : \mu \neq 16$ ounces
$\mathrm { H } _ { \mathrm { a } } : \mu = 16$ ounces

Question 13

Solve the problem.

-The owner of a football team claims that the average attendance at games is over 611, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

A)There is not sufficient sample evidence to support the claim that the mean attendance is greater than 611.
B)There is not sufficient sample evidence to support the claim that the mean attendance is less than 611.
C)There is sufficient sample evidence to support the claim that the mean attendance is less than 611.
D)There is sufficient sample evidence to support the claim that the mean attendance is greater than than 611.

Question 14

Solve the problem.

-The principal of a middle school claims that the test scores of the seventh-graders at his school vary less than the test scores of the seventh-graders at a neighboring school, which have a standard deviation of 14.6.
Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

A)There is sufficient sample evidence to support the claim that the standard deviation is greater than 14.6.
B)There is sufficient sample evidence to support the claim that the standard deviation is less than 14.6.
C)There is not sufficient sample evidence to support the claim that the standard deviation is less than 14.6.
D)There is not sufficient sample evidence to support the claim that the standard deviation is greater than 14.6.

Question 15

Formulate the null and alternative hypotheses for a hypothesis test.


-A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 1 in every one thousand.

A) $\mathrm { H } _ { 0 } : \mathrm { p } = 0.001$
$\mathrm { H } _ { \mathrm { a } } : \mathrm { p } < 0.001$

B) $\mathrm { H } _ { 0 } : \mathrm { p } > 0.001$
$\mathrm { H } _ { \mathrm { a } } : \mathrm { p } = 0.001$

C) $\mathrm { H } _ { 0 } : \mathrm { p } = 0.001$
$\mathrm { H } _ { \mathrm { a } } : \mathrm { p } > 0.001$

D) $\mathrm { H } _ { 0 } : \mathrm { p } < 0.001$
$\mathrm { H } _ { \mathrm { a } } : \mathrm { p } = 0.001$

Question 16

In 1990, the average math SAT score for students at one school was 498. Five years later, a teacher wants to perform a hypothesis test to determine whether the average math SAT score of students at the school has changed from the 1990 mean of 498.

A) $\mathrm { H } _ { 0 } : \mu = 498$
$\mathrm { H } _ { \mathrm { a } } : \mu < 498$

B) $\mathrm { H } _ { 0 } : \mu = 498$
$\mathrm { H } _ { \mathrm { a } } : \mu \neq 498$

C) $\mathrm { H } _ { 0 } : \mu = 498$
$\mathrm { H } _ { \mathrm { a } } : \mu > 498$

D) $\mathrm { H } _ { 0 } : : \mu \geq 498$
$\mathrm { H } _ { \mathrm { a } } : \mu < 498$

Question 17

Solve the problem.

-A cereal company claims that the mean weight of the cereal in its packets is at least 17 ounces. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the
Conclusion in nontechnical terms.

A)There is sufficient sample evidence to warrant rejection of the claim that the mean weight is less than 17 ounces.
B)There is not sufficient sample evidence to warrant rejection of the claim that the mean weight is less than 17 ounces.
C)There is not sufficient sample evidence to to support the claim that the mean weight is at least 17 ounces.
D)There is sufficient sample evidence to support the claim that the mean weight is at least 17 ounces.

Question 18

Solve the problem.

-A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 3 in every ten thousand. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

A)There is not sufficient sample evidence to support the claim that the proportion is greater than 3 in ten thousand.
B)There is sufficient sample evidence to support the claim that the proportion is greater than 3 in ten thousand.
C)There is sufficient sample evidence to support the claim that the proportion is less than 3 in ten thousand.
D)There is not sufficient sample evidence to support the claim that the proportion is less than 3 in ten thousand.

Question 19

Solve the problem.

-A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the 3.1 milligrams claimed by the manufacturer. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

A)There is not sufficient sample evidence to support the claim that the standard deviation is different from 3.1 milligrams.
B)There is sufficient sample evidence to support the claim that the standard deviation is equal to 3.1 milligrams.
C)There is sufficient sample evidence to support the claim that the standard deviation is different from 3.1 milligrams.
D)There is not sufficient sample evidence to support the claim that the standard deviation is equal to 3.1 milligrams.

Question 20

Answer the question.

-A study of a brand of "in the shell" peanuts sold at sports events gives the following results: $$\begin{array} { l | l } \text { Number of } & \\\text { Peanuts per bag}& \text { balprobability } \\ \hline 25 & 0.003 \\30 & 0.02 \\35 & 0.09 \\40 & 0.15 \\45 & 0.35 \\50 & 0.217 \\55 & 0.07\end{array}$$ A fan purchased a bag with 45 peanuts. Is this result significant at the 0.01 level?

A)Yes
B)No

Question 21

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a mean different from the 600 milligrams claimed by the manufacturer. The mean acetaminophen content for a random sample
Of 48 tablets is 603.3 milligrams. Test whether the claim that the mean amount of acetaminophen is different from 600 milligrams is supported or not supported. Assume that the population standard deviation is 4.9 milligrams.

A)not supported
B)supported

Question 22

Find the value of the standard score, z, and determine whether the alternative hypothesis is supported or not supported at a 0.05 significance level.

- $$\mathrm { H } _ { \mathrm { a } } : \mu > 50 , \mathrm { n } = 55 , \overline { \mathrm { x } } = 51 , \sigma = 3.6$$

A) $z = 3.29$ ; not supported
B) $z = 6.25$ ; supported
C) $z = 2.06$ ; supported
D) $z = 2.06$ ; not supported

Question 23

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-In the past, the mean running time for a certain type of flashlight battery has been 8.7 hours. The manufacturer has introduced a change in the production method which he hopes has increased the mean running time. The mean running time for a random sample of 40 light bulbs was 8.9 hours. Test whether the claim that the mean running time of all light bulbs has increased from the previous mean of 8.7 hours is supported or not supported. Assume that ? = 0.5 hours.

A)not supported
B)supported

Question 24

Find the value of the standard score, z, and determine whether the alternative hypothesis is supported or not supported at a 0.05 significance level.

- $$\mathrm { H } _ { \mathrm { a } } : \mu \neq 23 , \mathrm { n } = 60 , \overline { \mathrm { x } } = 25 , \sigma = 1.5$$

A) $z = 10.33$ ; not supported
B) $z = 10.33$ ; supported
C) $\mathrm { z } = - 1.96$ ; not supported
D) $z = 1.5$ ; not supported

Question 25

Use the partial table below to find the P-value that corresponds to the standard z-score, and determine whether the
alternative hypothesis is supported or not supported at the 0.05 significance level. $\underline{\text { Standard Score and Percentiles for a Normal Distribution }}$
$\begin{array}{rlrlll}\underline{Z }&\underline{ \% }\ &\underline{ Z }& \underline{\% }&\underline{Z }& \underline{\%}\\ -3.5 & 0.02 & -1.0 & 15.87 & 1.5 & 93.32 \\-3.0 & 0.13 & -0.5 & 30.85 & 2.0 & 97.72 \\-2.5 & 0.62 & 0.0 & 50.00 & 2.5 & 99.38 \\-2.0 & 2.28 & 0.5 & 69.15 & 3.0 & 99.87 \\-1.5 & 6.68 & 1.0 & 84.13 & 3.5 & 99.98\end{array}$


- $$\mathrm { z } = 3.5 \text { for } \mathrm { H } _ { \mathrm { a } } : \mu \neq 37.9$$

A) $0.0002$ ; supported
B) $0.9998$ ; supported
C) $0.0004$ ; supported
D) $0.0004$ ; not supported

Question 26

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-In one city, the average amount of time that tenth-graders spend watching television each week is 22.4 hours. the principal of Birchwood High School believes that at his school, tenth-graders watch less television. For a
Sample of 32 tenth-graders from Birchwood High School, the mean amount of time spent watching television per week was 20.2 hours. Test whether the claim that for all tenth-graders at Birchwood High School, the mean
Amount of time spent watching television per week is less than the city average of 22.4 hours is supported or not supported. Assume that $\sigma = 7.2$
Hours.

A)not supported
B)supported

Question 27

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200.
The insurer wants to perform a hypothesis test to determine whether their suspicion is correct. The mean fee charged by the clinic for a random sample of 65 patients receiving this procedure was $1280. Test whether the claim that the mean fee charged by this particular clinic is higher than $1200 is supported or not supported. Assume that $\sigma = \$ 210$

A)not supported
B)supported

Question 28

Use the partial table below to find the P-value that corresponds to the standard z-score, and determine whether the
alternative hypothesis is supported or not supported at the 0.05 significance level. $\underline{\text { Standard Score and Percentiles for a Normal Distribution }}$
$\begin{array}{rlrlll}\underline{Z }&\underline{ \% }\ &\underline{ Z }& \underline{\% }&\underline{Z }& \underline{\%}\\ -3.5 & 0.02 & -1.0 & 15.87 & 1.5 & 93.32 \\-3.0 & 0.13 & -0.5 & 30.85 & 2.0 & 97.72 \\-2.5 & 0.62 & 0.0 & 50.00 & 2.5 & 99.38 \\-2.0 & 2.28 & 0.5 & 69.15 & 3.0 & 99.87 \\-1.5 & 6.68 & 1.0 & 84.13 & 3.5 & 99.98\end{array}$


- $$z = 2.0 \text { for } H _ { a } : \mu > 31.28$$

A) $0.0228$ ; not supported
B) $0.9772$ ; not supported
C) $0.0228$ ; supported
D) $0.9772$ ; supported

Question 29

Find the value of the standard score, z, and determine whether the alternative hypothesis is supported or not supported at a 0.05 significance level.

- $$\mathrm { H } _ { \mathrm { a } } : \mu < 10 , \mathrm { n } = 18 , \overline { \mathrm { x } } = 7.5 , \sigma = 1.7$$

A) $z = 7.5$ ; supported
B) $z = - 6.24$ ; supported
C) $z = - 6.24$ ; not supported
D) $z = 1.7 . ;$ supported

Question 30

Use the partial table below to find the P-value that corresponds to the standard z-score, and determine whether the
alternative hypothesis is supported or not supported at the 0.05 significance level. $\underline{\text { Standard Score and Percentiles for a Normal Distribution }}$
$\begin{array}{rlrlll}\underline{Z }&\underline{ \% }\ &\underline{ Z }& \underline{\% }&\underline{Z }& \underline{\%}\\ -3.5 & 0.02 & -1.0 & 15.87 & 1.5 & 93.32 \\-3.0 & 0.13 & -0.5 & 30.85 & 2.0 & 97.72 \\-2.5 & 0.62 & 0.0 & 50.00 & 2.5 & 99.38 \\-2.0 & 2.28 & 0.5 & 69.15 & 3.0 & 99.87 \\-1.5 & 6.68 & 1.0 & 84.13 & 3.5 & 99.98\end{array}$


- $\mathrm { z } = - 2.5$ for $\mathrm { H } _ { \mathrm { a } } : \mu < 22$

A) $0.0062$ ; supported
B) $0.9938$ ; not supported
C) $0.9938$ ; supported
D) $0.0062$ ; not supported

Question 31

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The mean volume of juice for a random sample of 70 bottles was 15.94 ounces. Test whether the claim that the mean amount of juice for all 16-ounce bottles is less than 16.1 ounces is supported or not supported. Assume that ? = 0.9 ounces.

A)supported
B)not supported

Question 32

Use the partial table below to find the P-value that corresponds to the standard z-score, and determine whether the
alternative hypothesis is supported or not supported at the 0.05 significance level. $\underline{\text { Standard Score and Percentiles for a Normal Distribution }}$
$\begin{array}{rlrlll}\underline{Z }&\underline{ \% }\ &\underline{ Z }& \underline{\% }&\underline{Z }& \underline{\%}\\ -3.5 & 0.02 & -1.0 & 15.87 & 1.5 & 93.32 \\-3.0 & 0.13 & -0.5 & 30.85 & 2.0 & 97.72 \\-2.5 & 0.62 & 0.0 & 50.00 & 2.5 & 99.38 \\-2.0 & 2.28 & 0.5 & 69.15 & 3.0 & 99.87 \\-1.5 & 6.68 & 1.0 & 84.13 & 3.5 & 99.98\end{array}$


- $\mathrm { z } = - 2.5$ for $\mathrm { H } _ { \mathrm { a } } : \mu \neq 0.861$

A) $0.0124$ ; supported
B) $0.0124$ ; not supported
C) $0.9876$ ; supported
D) $0.0062$ ; supported

Question 33

Use the partial table below to find the P-value that corresponds to the standard z-score, and determine whether the
alternative hypothesis is supported or not supported at the 0.05 significance level. $\underline{\text { Standard Score and Percentiles for a Normal Distribution }}$
$\begin{array}{rlrlll}\underline{Z }&\underline{ \% }\ &\underline{ Z }& \underline{\% }&\underline{Z }& \underline{\%}\\ -3.5 & 0.02 & -1.0 & 15.87 & 1.5 & 93.32 \\-3.0 & 0.13 & -0.5 & 30.85 & 2.0 & 97.72 \\-2.5 & 0.62 & 0.0 & 50.00 & 2.5 & 99.38 \\-2.0 & 2.28 & 0.5 & 69.15 & 3.0 & 99.87 \\-1.5 & 6.68 & 1.0 & 84.13 & 3.5 & 99.98\end{array}$


- $$\mathrm { z } = 0.5 \text { for } \mathrm { H } _ { \mathrm { a } } : \mu > 60$$

A) $0.3085$ ; not supported
B) 0.3085; supported
C) $0.6915$ ; not supported
D) $0.6915$ ; supported

Question 34

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-In 1990, the average math SAT score for students at one school was 475. Five years later, a teacher wants to perform a hypothesis test to determine whether the average math SAT score of students at the school has changed. He picks a random sample of 60 students and obtains their mean math SAT score, which is 469. Test whether the claim that the average math SAT score at the school has dropped from 475 is supported or not
Supported. Assume that $\sigma = 73$

A)not supported
B)supported

Question 35

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-In 1990, the average duration of long-distance telephone calls originating in one town was 9.8 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.8 minutes. The mean duration for a random sample of 50 calls originating in the town was 9.0 minutes. Test whether the claim that the mean call duration is less than the 1990 mean of 9.8 minutes is supported or not supported. Assume that ? = 4.8 minutes.

A)not supported
B)supported

Question 36

Find the value of the standard score, z, and determine whether the alternative hypothesis is supported or not supported at a 0.05 significance level.

- $\mathrm { H } _ { \mathrm { a } } : \mu \neq 18.7 , \mathrm { n } = 11 , \overline { \mathrm { x } } = 20.5 , \sigma = 7$

A) $z = - 0.85$ ; supported
B) $z = - 0.85$ ; not supported
C) $\mathrm { z } = 0.85$ ; supported
D) $z = 0.85$ ; not supported

Question 37

Find the value of the standard score, z, and determine whether the alternative hypothesis is supported or not supported at a 0.05 significance level.

- $\mathrm { H } _ { \mathrm { a } } : \mu < 56 , \mathrm { n } = 37 , \overline { \mathrm { x } } = 54 , \sigma = 5.6$

A) $\mathrm { z } = - 2.17$ ; supported
B) $z = 2.17$ ; supported
C) $z = 5.14$ ; supported
D) $z = - 2.17$ ; not supported

Question 38

Answer the question.

-A study of a brand of "in the shell" peanuts sold at sports events gives the following results: $$\begin{array} { l | l } \text { Number of } & \\\text { Peanuts per bag}& \text {probability } \\ \hline 25 & 0.003 \\30 & 0.02 \\35 & 0.09 \\40 & 0.15 \\45 & 0.35 \\50 & 0.217 \\55 & 0.07\end{array}$$ A fan purchased a bag with 35 peanuts. Is there a low or high likelihood of getting 35 peanuts by chance?

A)low
B)high

Question 39

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-A brochure claims that the average maximum height of a certain type of plant is 0.7 meters. A gardener suspects that this estimate is not accurate locally due to soil conditions. A random sample of 48 mature plants is taken.
The mean height of the plants in the sample is 0.65 meters. Test whether the claim that the average maximum height is different from 0.7 meters is supported or not supported. Assume that the standard deviation is
0.2 meters.

A)supported
B)not supported

Question 40

Use the partial table below to find the P-value that corresponds to the standard z-score, and determine whether the
alternative hypothesis is supported or not supported at the 0.05 significance level. $\underline{\text { Standard Score and Percentiles for a Normal Distribution }}$
$\begin{array}{rlrlll}\underline{Z }&\underline{ \% }\ &\underline{ Z }& \underline{\% }&\underline{Z }& \underline{\%}\\ -3.5 & 0.02 & -1.0 & 15.87 & 1.5 & 93.32 \\-3.0 & 0.13 & -0.5 & 30.85 & 2.0 & 97.72 \\-2.5 & 0.62 & 0.0 & 50.00 & 2.5 & 99.38 \\-2.0 & 2.28 & 0.5 & 69.15 & 3.0 & 99.87 \\-1.5 & 6.68 & 1.0 & 84.13 & 3.5 & 99.98\end{array}$


- $$\mathrm { z } = - 0.5 \text { for } \mathrm { H } _ { \mathrm { a } } : \mu < 60$$

A) 0.3085; supported
B) $0.3085$ ; not supported
C) $0.6915$ ; not supported
D) $0.6915$ ; supported

Question 41

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-In 1990, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes. The mean duration for a random sample of 50 calls originating in the town was 8.6 minutes. Test whether the claim that the mean call duration has changed from the 1990 mean of 9.4 minutes is supported or not supported. Assume that the
Population standard deviation is 4.5 minutes.

A)supported
B)not supported

Question 42

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-A researcher wants to check the claim that convicted burglars spend an average of 15.7 months in jail. She takes a random sample of 35 such cases from court files and finds that the mean time in jail is 13.7 months. Test whether the claim that the average jail time for convicted burglars is different from 15.7 months is supported or not supported. Assume that the population standard deviation is 7 months.

A)supported
B)not supported

Question 43

Identify the Type I error or Type II error as indicated.

-In 1990, the average math SAT score for students at one school was 483. Five years later, a teacher wants to perform a hypothesis test to determine whether the average math SAT score of students at the school has changed from the 1990 mean of 483. The hypotheses are: $$\begin{array} { l } \mathrm { H } _ { 0 } : \mu = 483 \\\mathrm { H } _ { a } : \mu \neq 483\end{array}$$
Identify the Type I error.

A)Fail to reject the claim that the average math SAT score is 483 when in fact it is 483.
B)Reject the claim that the average math SAT score is 483 when in fact it is 483.
C)Reject the claim that the average math SAT score is 483 when in fact it is not 483.
D)Fail to reject the claim that the average math SAT score is 483 when in fact it is not 483.

Question 44

Find the P-value for the indicated hypothesis test. Round all proportions and standard scores to two decimal places.

-A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 130 of the school's students, 31% of them plan to go into general practice. Find the
P-value for a test of the school's claim.

A)0.2263
B)0.4472
C)0.2236
D)0.7764

Question 45

Find the P-value for the indicated hypothesis test. Round all proportions and standard scores to two decimal places.

-In a sample of 47 adults selected randomly from one town, it is found that 10 of them have been exposed to a particular strain of the flu. Find the P-value for a test of the claim that the proportion of all adults in the town that have been exposed to this strain of the flu is 8%.

A)0.001
B)0.0005
C)0.099
D)0.01

Question 46

Use a 0.05 significance level and conduct a full hypothesis test. List the null and alternative hypotheses, the z-score, the P-value, and whether to reject or not reject the null hypothesis. Round z-scores to the nearest tenth.

-In tests of a computer component, it is found that the mean time between failures is 937 hours. A modification is made which is supposed to increase reliability by increasing the time between failures. Tests on a sample of 36 modified components produce a mean time between failures of 960 hours, with a standard deviation of 52 hours. Test the claim that for the modified components, the mean time between failures is greater than 937 hours.

Question 47

Use a 0.05 significance level and conduct a full hypothesis test. List the null and alternative hypotheses, the z-score, the P-value, and whether to reject or not reject the null hypothesis. Round z-scores to the nearest tenth.

-A manufacturer makes steel rods that are supposed to have a mean length of 50 centimeters. A retailer suspects that the bars are running short. The mean length for a random sample of 34 bars was 48.4 centimeters with a standard deviation of 3.6 centimeters. Test the claim that the mean length is less than 50
centimeters.

Question 48

Identify the Type I error or Type II error as indicated.

-The average diastolic blood pressure of a group of men suffering from high blood pressure is 100 mmHg. During a clinical trial, the men receive a medication which it is hoped will lower their blood pressure. After three
Months, the researcher wants to perform a hypothesis test to determine whether the average diastolic blood pressure of
The men has decreased. The hypotheses are: $$\begin{array} { l } \mathrm { H } _ { 0 } : \mu = 100 \mathrm { mmHg } \\\mathrm { H } _ { \mathrm { a } } : \mu < 100 \mathrm { mmHg }\end{array}$$
Identify the Type II error.

A)Fail to reject the claim that the average diastolic blood pressure is 100 mmHg when in fact it is less than 100 mmHg.
B)Fail to reject the claim that the average diastolic blood pressure is 100 mmHg when in fact it is 100 mmHg.
C)Reject the claim that the average diastolic blood pressure is 100 mmHg when in fact it is 100 mmHg.
D)Reject the claim that the average diastolic blood pressure is 100 mmHg when in fact it is less than 100 mmHg.

Question 49

Identify the Type I error or Type II error as indicated.

-In the past, the mean running time for a certain type of flashlight battery has been 8.3 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the
Mean running time has increased as a result. The hypotheses are: $$\begin{array} { l } \mathrm { H } _ { 0 } : \mu = 8.3 \text { hours } \\\mathrm { H } _ { \mathrm { a } } : \mu > 8.3 \text { hours }\end{array}$$
Identify the Type II error.

A)Fail to reject the claim that the mean running time is 8.3 hours when actually the mean running time is greater than 8.3 hours.
B)Reject the claim that the mean running time is 8.3 hours when actually the mean running time is greater than 8.3 hours.
C)Fail to reject the claim that the mean running time is 8.3 hours when actually the mean running time is 8.3 hours.
D)Reject the claim that the mean running time is 8.3 hours when actually the mean running time is 8.3 hours.

Question 50

Find the P-value for the indicated hypothesis test. Round all proportions and standard scores to two decimal places.

-A manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of 97 such fax machines, 3% are defective. Find the P-value for a test of the manufacturer's claim.

A)0.1057
B)0.1075
C)0.0108
D)0.215

Question 51

Identify the Type I error or Type II error as indicated.

-A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The
Hypotheses are:

$$\begin{array} { l } \mathrm { H } _ { 0 } : \mu = 16.1 \text { ounces } \\\mathrm { H } _ { \mathrm { a } } : \mu < 16.1 \text { ounces }\end{array}$$
Identify the Type I error.

A)Reject the claim that mean amount is 16.1 ounces when in fact the mean amount is less than 16.1 ounces.
B)Fail to reject the claim that mean amount is 16.1 ounces when in fact the mean amount is less than 16.1 ounces.
C)Reject the claim that mean amount is 16.1 ounces when in fact the mean amount is 16.1 ounces.
D)Fail to reject the claim that mean amount is 16.1 ounces when in fact the mean amount is 16.1 ounces.

Question 52

Use a 0.05 significance level and conduct a full hypothesis test. List the null and alternative hypotheses, the z-score, the P-value, and whether to reject or not reject the null hypothesis. Round z-scores to the nearest tenth.

-A national car insurance company stated that in 1987, the average yearly car insurance cost for a family in the U.S. was $1716. In the same year, a random sample of 32 families in California resulted in a mean cost of $1728
with a standard deviation of $35.50. Test the claim that the average insurance cost for a family in California in 1987 exceeded the national average.

Question 53

Identify the Type I error or Type II error as indicated.

-In the past, the mean running time for a certain type of flashlight battery has been 8.9 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the
Mean running time has increased as a result. The hypotheses are: $$\begin{array} { l } \mathrm { H } _ { 0 } : \mu = 8.9 \text { hours } \\\mathrm { H } _ { \mathrm { a } } : \mu > 8.9 \text { hours }\end{array}$$
Identify the Type I error.

A)Reject the claim that the mean running time is 8.9 hours when actually the mean running time is greater than 8.9 hours.
B)Reject the claim that the mean running time is 8.9 hours when actually the mean running time is 8.9 hours.
C)Fail to reject the claim that the mean running time is 8.9 hours when actually the mean running time is greater than 8.9 hours.
D)Fail to reject the claim that the mean running time is 8.9 hours when actually the mean running time is 8.9 hours.

Question 54

Find the P-value for the indicated hypothesis test. Round all proportions and standard scores to two decimal places.

-In a sample of 88 children selected randomly from one town, it is found that 8 of them suffer from asthma. Find the P-value for a test of the claim that the proportion of all children in the town who suffer from asthma is equal
To 11%.

A)0.2743
B)0.2473
C)0.5468
D)0.5486

Question 55

Find the P-value for the indicated hypothesis test. Round all proportions and standard scores to two decimal places.

-An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Littleton. A random sample of 250 fathers from
Littleton yielded 97 who did not help with child care. Find the P-value for a test of the researcher's claim.

A)0.475
B)0.0475
C)0.0745
D)0.095

Question 56

Use a 0.05 significance level and conduct a full hypothesis test. List the null and alternative hypotheses, the z-score, the P-value, and whether to reject or not reject the null hypothesis. Round z-scores to the nearest tenth.

-A department store accepts only its own credit card. Among 36 randomly selected card holders, it was found that the mean amount owed was $175.37, while the standard deviation was $84.77. Test the claim that the mean amount owed by all customers is greater than $150.00.

Question 57

Identify the Type I error or Type II error as indicated.

-In 1990, the average math SAT score for students at one school was 500. Five years later, a teacher wants to perform a hypothesis test to determine whether the average SAT score of students at the school has changed from the 1990 mean of 500. The hypotheses are: $$\begin{array} { l } \mathrm { H } _ { 0 } : \mu = 500 \\\mathrm { H } _ { \mathrm { a } } : \mu \neq 500\end{array}$$
Identify the Type II error.

A)Reject the claim that the average math SAT score is 500 when in fact it is not 500.
B)Fail to reject the claim that the average math SAT score is 500 when in fact it is not 500.
C)Fail to reject the claim that the average math SAT score is 500 when in fact it is 500.
D)Reject the claim that the average math SAT score is 500 when in fact it is 500.

Question 58

Use a 0.05 significance level and conduct a full hypothesis test. List the null and alternative hypotheses, the z-score, the P-value, and whether to reject or not reject the null hypothesis. Round z-scores to the nearest tenth.

-A customer claims that the mean amount of time customers spend waiting in line is 3.7 minutes. The manager of the store runs a test and finds a mean waiting time for a random sample of 120 customers of 3.6 minutes with
a standard deviation of 1.1 minutes. Test the manager's claim that the mean customer waiting time is less than 3.7 minutes.

Question 59

Use a 0.05 significance level and conduct a full hypothesis test. List the null and alternative hypotheses, the z-score, the P-value, and whether to reject or not reject the null hypothesis. Round z-scores to the nearest tenth.

-The National Association of Realtors reported that the mean selling price last year for homes in one city was $116,800. The city housing department feels that this figure is too low. They randomly selected 91 home sales and obtained a mean selling price of $117,900 and a standard deviation of $3700. Test the claim that the mean selling price was $116,800.

Question 60

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-In 1990, the average math SAT score for students at one school was 475. Five years later, a teacher wants to perform a hypothesis test to determine whether the average math SAT score of students at the school has changed. He picks a random sample of 40 students and obtains their the mean math SAT score, which is 472.
Test whether the claim that the mean math SAT score for all students at the school has changed from the previous mean of 475 is supported or not supported. Assume that the population standard deviation is 73.

A)not supported
B)supported

Question 61

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-A medical school claims that more than 28% of its students plan to go into general practice. It is found that
Among a random sample of 130 of the school's students, 31% of them plan to go into general practice. Test
Whether the school's claim is supported or not supported.

A)not supported
B)supported

Question 62

Find the P-value for the indicated hypothesis test. Round all proportions and standard scores to two decimal places.

-A nationwide study of American homeowners revealed that 65% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Find the P-value for a test of the claim that the proportion with lawn mowers in Omaha is higher than 65%. Among 497 randomly selected homes in Omaha, 338 had one or more lawn mowers.

A)0.0808
B)0.8080
C)0.9192
D)0.0404

Question 63

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-A supplier of 3.5" disks claims that no more than 1% of the disks are defective. In a random sample of 700 disks, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. Test whether the supplier's claim that no more than 1% are defective is supported or not supported.

A)not supported
B)supported

Question 64

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher
Claims that the figure is higher for fathers in the town of Littleton. A random sample of 225 fathers from
Littleton yielded 97 who did not help with child care. Test whether the researcher's claim that the percentage is
Higher than 34% is supported or not supported.

A)not supported
B)supported

Question 65

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect rate is 5.8% but the manager claims that this is only a sample fluctuation and production is not really out of control. Test whether the manufacturer's claim that production is out of control is supported or not supported.

A)supported
B)not supported

Question 66

Find the P-value for the indicated hypothesis test. Round all proportions and standard scores to two decimal places.

-A random sample of 140 forty-year-old men contains 26% who smoke. Find the P-value for a test of the claim that the percentage of forty-year-old men that smoke is 22%.

A)0.1401
B)0.2542
C)0.2802
D)0.1271

Question 67

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-In a sample of 47 adults selected randomly from one town, it is found that 10 of them have been exposed to a particular strain of the flu. Test whether the claim that the proportion of all all adults exposed to this strain is different from 8% is supported or not supported.

A)not supported
B)supported

Question 68

Find the P-value for the indicated hypothesis test. Round all proportions and standard scores to two decimal places.

-An airline claims that the no-show rate for passengers booked on its flights is less than 6%. Of 380 randomly selected reservations, 18 were no-shows. Find the P-value for a test of the airline's claim.

A)0.7939
B)0.2061
C)0.4122
D)0.0206

Question 69

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-A poll of 1065 adult Americans reveals that 48% of the voters surveyed prefer the Democratic candidate for the presidency. Test whether the claim that less than half of all voters prefer the Democrat is supported or not supported.

A)supported
B)not supported

Question 70

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-According to a recent poll 53% of Americans would vote for the incumbent president. If a random sample of 100 people results in 25% who would vote for the incumbent, test whether the claim that the actual percentage is different from 53% is supported or not supported.

A)supported
B)not supported

Question 71

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.

-A nationwide study of American homeowners revealed that 65% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Among 497 randomly selected homes in Omaha, 340 had one or more lawn mowers. Test whether the manufacturer's claim that the percentage is greater than 65% is supported or not supported.

A)not supported
B)supported