Deck 8: Hypothesis Testing

Question 1

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. The principal of a middle school claims that 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 variation described by 7. 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 evidence to support the claim that the standard deviation is greater than 14.7.
B) There is not sufficient evidence to support the claim that the standard deviation is less than 14.7.
C) There is sufficient evidence to support the claim that the standard deviation is greater than 14.7.
D) There is sufficient evidence to support the claim that the standard deviation is less than 14.7.

Answer 1

D

Question 2

Answer 2

D

Question 3

Suppose we want to test the claim that the majority of adults are in favor of raising the voting age to 21. Is the hypothesis test left-tailed, right-tailed, or two-tailed?

A) Two-tailed
B) Left-tailed
C) Right-tailed

Answer 3

C

Question 4

Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). With : p > 0.554, the test
Statistic is z = 1.34.

A) 0.0901; fail to reject the null hypothesis
B) 0.9099; fail to reject the null hypothesis
C) 0.1802; reject the null hypothesis
D) 0.0901; reject the null hypothesis

Question 5

Question 6

A) 7.015
B) 8.231
C) 31.526
D) 8.907

Question 7

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. Carter Motor Company claims that its new sedan, the Libra, will average better than 32 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 sufficient evidence to support the claim that the mean is less than 32 miles per gallon.
B) There is not sufficient evidence to support the claim that the mean is greater than 32 miles per gallon.
C) There is not sufficient evidence to support the claim that the mean is less than 32 miles per gallon.
D) There is sufficient evidence to support the claim that the mean is greater than 32 miles per gallon.

Question 8

The ________ is the probability of getting a test statistic at least as extreme as the one representing the sample data, assuming that the null hypothesis is true.

A) critical value
B) P-value
C) level of significance
D) sample proportion

Question 9

Find the P-value in a test of the claim that the mean IQ score of acupuncturists is equal to 100, given that the test statistic is z = -2.00.

Question 10

Which of the following is not a requirement for testing a claim about a population proportion?

A)
B) The conditions for a binomial distribution are satisfied.
C) The sample observations are a simple random sample.
D) All of the other statements are requirements for testing a claim about a population proportion.

Question 11

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol ( for the indicated parameter. A psychologist claims that more than 5.8 percent of the population suffers from
Professional problems due to extreme shyness. Use p, the true percentage of the population that suffers from
Extreme shyness.

Question 12

Express the original claim in symbolic form. Claim: 20% of adults smoke

Question 13

A Type I error is the mistake of ________ when it is actually true.

A) rejecting the alternative hypothesis
B) rejecting the null hypothesis
C) failing to reject the alternative hypothesis
D) failing to reject the null hypothesis

Question 14

Question 15

A chi-square hypothesis test is going to be conducted about a population standard deviation. Select the statement that is not true about the Chi-square test.

A) The population does not have to be a normally distributed population.
B) The sample must be a simple random sample.
C) The sample size must be known.
D) The alternative hypothesis must contain

Question 16

A) 30.813
B) 14.848
C) 14.042
D) -30.813

Question 17

A hypothesis test is performed to test the claim that a population proportion is greater than 0.7. Find the probability of a type II error, β, given that the true value of the population proportion is 0.72. The sample size is
50 and the significance level is 0.05.

A) 0.4129
B) 0.7123
C) 0.9706
D) 0.5754

Question 18

Question 19

Find the value of the test statistic z using The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, and the sample statistics include n = 696 drowning deaths of children with 30% of them attributable to beaches.

A) 2.88
B) -2.88
C) 3.05
D) -3.05

Question 20

Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). The test statistic in a
Right-tailed test is z = 0.52.

A) 0.6030; fail to reject the null hypothesis
B) 0.3015; fail to reject the null hypothesis
C) 0.0195; reject the null hypothesis
D) 0.3015; reject the null hypothesis

Question 21

Question 22

A ________ error is the mistake of rejecting the null hypothesis when it is actually true.

A) Type I
B) Type II
C) Type III
D) Type IV

Question 23

The p-value is the probability of getting a test statistic at least as extreme as the one representing the sample data, assuming that ________.

A) the alternative hypothesis is true
B) the null hypothesis is true
C) the alternative hypothesis is false
D) the null hypothesis is false

Question 24

Which of the following is a requirement for testing a claim about a population proportion?

A)
B) The trials are dependent.
C) The sample observations are a stratified sample.
D) None of the other statements are requirements for testing a claim about a population proportion.

Question 25

Question 26

Suppose we want to test the claim that less than ½ of Americans are in favor of raising the voting age to 21. Is the hypothesis test left-tailed, right-tailed, or two-tailed?

A) Two-tailed
B) Right-tailed
C) Left-tailed

Question 27

Question 28

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. Carter Motor Company claims that its new sedan, the Libra, will average better than 32 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 evidence to support the claim that the mean is less than 32 miles per gallon.
B) There is not sufficient evidence to support the claim that the mean is greater than 32 miles per gallon.
C) There is sufficient evidence to support the claim that the mean is less than 32 miles per gallon.
D) There is sufficient evidence to support the claim that the mean is greater than 32 miles per gallon.

Question 29

Question 30

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. The owner of a football team claims that the average attendance at games is over 523, 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 evidence to support the claim that the mean attendance is greater than 523.
B) There is sufficient evidence to support the claim that the mean attendance is greater than 523.
C) There is not sufficient evidence to support the claim that the mean attendance is less than 523.
D) There is sufficient evidence to support the claim that the mean attendance is less than 523.

Question 31

Express the original claim in symbolic form. Claim: 60% of homes have smoke detectors.

Question 32

Find the value of the test statistic z using A claim is made that the proportion of children who play sports is less than 0.5, and the sample statistics include n = 1320 subjects with 30% saying that they play a sport.

A) -29.66
B) 29.66
C) 14.53
D) -14.53

Question 33

Find the P-value for the indicated hypothesis test. 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. Find the
P-value for a test of the researcher's claim.

A) 0.0019
B) 0.0529
C) 0.0038
D) 0.0015

Question 34

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (µ, p, σ) for the indicated parameter. The manufacturer of a refrigerator system for beer kegs produces refrigerators that are
Supposed to maintain a true mean temperature, µ, 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 true
Mean temperature is incorrect.

Question 35

Question 36

Question 37

Find the P-value in a test of the claim that the mean College Algebra final exam score of engineering majors equal to 88, given that the test statistic is z = 1.50.

A) 0.0668
B) 0.1500
C) 0.9331
D) 0.1336

Question 38

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. A consumer advocacy group claims that the mean mileage for the Carter Motor Company's new sedan is
Less than 32 miles per gallon. Identify the type I error for the test.

A) Fail to reject the claim that the mean is equal to 32 miles per gallon when it is actually greater than 32 miles per gallon.
B) Reject the claim that the mean is equal to 32 miles per gallon when it is actually less than 32 miles per gallon.
C) Reject the claim that the mean is equal to 32 miles per gallon when it is actually 32 miles per gallon.
D) Fail to reject the claim that the mean is equal to 32 miles per gallon when it is actually less than 32 miles per gallon.

Question 39

Question 40

Question 41

Solve the problem. What do you conclude about the claim below? Do not use formal procedures or exact calculations.
Use only the rare event rule and make a subjective estimate to determine whether the event is likely.
Claim: A roulette wheel is fair and in 40 consecutive spins of the wheel, black shows up 23 times. (A roulette wheel has
38 equally likely slots of which 18 are black).

Question 42

Test the given claim. Use the P-value method or the traditional method as indicated. Identify the null
hypothesis, alternative hypothesis, test statistic, critical value(s) or P-value, conclusion about the null
hypothesis, and final conclusion that addresses the original claim. The mean resting pulse rate for men is 72
beats per minute. A simple random sample of men who regularly work out at Mitch's Gym is obtained and their
resting pulse rates (in beats per minute) are listed below. Use a 0.05 significance level to test the claim that these
sample pulse rates come from a population with a mean less than 72 beats per minute. Assume that the
standard deviation of the resting pulse rates of all men who work out at Mitch's Gym is known to be 6.6 beats
per minute. Use the traditional method of testing hypotheses.

Question 43

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and
that the sample has been randomly selected. Heights of men aged 25 to 34 have a standard deviation of 2.9. Use
a 0.05 significance level to test the claim that the heights of women aged 25 to 34 have a different standard
deviation. The heights (in inches) of 16 randomly selected women aged 25 to 34 are listed below. Round the
sample standard deviation to five decimal places.

Question 44

Solve the problem. Suppose that you are conducting a study on the effectiveness of a new teaching method and
that you wish to use a hypothesis test to support your claim regarding the mean test score under this method.
What restrictions are there in the wording of the claim? Will your claim become the null hypothesis or the
alternative hypothesis, or does it depend on the situation? Give an example of a claim which is incorrectly
worded.

Question 45

Assume that a simple random sample has been selected from a normally distributed population and test the
given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative
hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final
conclusion that addresses the original claim.
A cereal company claims that the mean weight of the cereal in its packets is 14 oz. The weights (in ounces) of the cereal
in a random sample of 8 of its cereal packets are listed below. Test the claim at the 0.01 significance level.

Question 46

Assume that a simple random sample has been selected from a normally distributed population and test the
given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative
hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final
conclusion that addresses the original claim. A light-bulb manufacturer advertises that the average life for its light
bulbs is 900 hours. At the 10% significance level, test the claim that the sample is from a population with a mean life of 900 hours. Use the
P-value method of testing hypotheses.

Question 47

Question 48

Provide an appropriate response. Complete the following table on hypothesis testing.

Question 49

Question 50

What do you conclude about the claim below? Do not use formal procedures or exact calculations. Use only the rare
event rule and make a subjective estimate to determine whether the event is likely.
Claim: A die is fair and in 100 rolls there are 63 sixes.

Question 51

Sam wanted to test a claim about the mean of a population whose standard deviation was unknown. He picked
a simple random sample of size 20 from the population. Lou wanted to test a claim about a mean of a different
population whose standard deviation was known. He picked a simple random sample of size 22 from that
population. George said that Sam would need to determine whether his sample was from a normally
distributed population because the population standard deviation was unknown. He said that Lou would not
need to do this since for his test the population standard deviation was known. Is George right?

Question 52

A simple random sample of the running time of movies of 70 international movies resulted in a sample mean
length of 112 minutes and a sample standard deviation of 7 minutes. Test the claim that international movies
have a mean running time of more than 110 minutes at the 5% level of significance. Assume that the lengths of
movies are normally distributed.

Question 53

An oil change shop claims that they will change your oil in under 15 minutes. To test this claim, a consumer
advocacy group takes a simple random sample of 10 customers and records the number of minutes it took to
complete oil changes for these customers. Assume that oil change times are normally distributed. Conduct a hypothesis test for the oil shop's claim about oil change times at the 5% level of significance.

Question 54

Solve the problem. Use the P-value method to test the claim that the population standard deviation of the
systolic blood pressures of adults aged 40-50 is equal to 22 mmHg. The sample statistics are as follows: n = 23, x
= 132.2 mmHg, s = 26.6 mmHg. Be sure to state the hypotheses, the value of this test statistic, the P-value, and
your conclusion. Use a significance level of 0.05.

Question 55

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis,
and final conclusion that addresses the original claim. 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 234 fathers from Littleton yielded 96 who did not help with child care. Test the
researcher's claim at the 0.05 significance level.

Question 56

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis,
and final conclusion that addresses the original claim. The health of employees is monitored by periodically
weighing them in. A sample of 54 employees has a mean weight of 183.9 lb. Assuming that σ is known to be
121.2 lb, use a 0.10 significance level to test the claim that the population mean of all such employees weights is
less than 200 lb.

Question 57

Question 58

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and
that the sample has been randomly selected. For randomly selected adults, IQ scores are normally distributed
with a standard deviation of 15. The scores of 14 randomly selected college students are listed below. Use a 0.10
significance level to test the claim that the standard deviation of IQ scores of college students is less than 15. Round
the sample standard deviation to three decimal places.

Question 59

Assume that a simple random sample has been selected from a normally distributed population and test the
given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative
hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final
conclusion that addresses the original claim. A public bus company official claims that the mean waiting time
for bus number 14 during peak hours is less than 10 minutes. Karen took bus number 14 during peak hours on
18 different occasions. Her mean waiting time was 7.6 minutes with a standard deviation of 2.3 minutes. At the
0.01 significance level, test the claim that the mean waiting time is less than 10 minutes. Use the P-value method
of testing hypotheses.

Question 60

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and
that the sample has been randomly selected. A manufacturer uses a new production method to produce steel
rods. A random sample of 17 steel rods resulted in lengths with a standard deviation of 4.7 cm. At the 0.10
significance level, test the claim that the new production method has lengths with a standard deviation different
from 3.5 cm, which was the standard deviation for the old method.

Question 61

Write the claim that is suggested by the given statement, then write a conclusion about the claim. Do not use
symbolic expressions or formal procedures; use common sense.
Last year an appliance manufacturer received many complaints about the high rate of defects among its
washing machines. Approximately 9% of the machines were defective in some way. This year the company
tightened up its quality control procedures. The latest shipment of 250 washing machines contained 2 defective
units.

Question 62

Carter Motor Company claims that its new sedan, the Libra, will average better than 23 miles per gallon in the city. Use the true average mileage of the Libra.

Question 63

Express the null hypothesis and the alternative hypothesis in symbolic form for a test to reject this claim. Use the correct
symbol for the indicated parameter.
A researcher claims that 62% of voters favor gun control.

Question 64

An entomologist writes an article in a scientific journal which claims that fewer than 16 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of
Fireflies unable to produce light.

Question 65

The principal of a middle school claims that test scores of the seventh-graders at her school vary less than the test scores of seventh-graders at a neighboring school, which have variation described by

Question 66

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 2 in every one thousand.

Question 67

The owner of a football team claims that the average attendance at games is over 68,800, and he is therefore justified in moving the team to a city with a larger stadium.

Question 68

What do you conclude about the claim below? Do not use formal procedures or exact calculations. Use only the
rare event rule and make a subjective estimate to determine whether the event is likely.
Claim: A die is fair and in 100 rolls there are 63 sixes.

Question 69

The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, µ, 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 true mean temperature is incorrect.

Question 70

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the 3.3 mg claimed by the manufacturer.

Question 71

What do you conclude about the claim below? Do not use formal procedures or exact calculations. Use only the
rare event rule and make a subjective estimate to determine whether the event is likely.
Claim: An employee of a company is equally likely to take a sick day on any day of the week. Last year, the total
number of sick days taken by all the employees of the company was 143. Of these, 52 were Mondays, 14 were
Tuesdays, 17 were Wednesdays, 17 were Thursdays, and 43 were Fridays.

Question 72

Express the null hypothesis and the alternative hypothesis in symbolic form for a test to reject this claim. Use the correct
symbol for the indicated parameter.
A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz.

Question 73

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z
value used to test a null hypothesis.

Question 74

Write the claim that is suggested by the given statement, then write a conclusion about the claim. Do not use
symbolic expressions or formal procedures; use common sense.
A math teacher tries a new method for teaching her introductory statistics class. Last year the mean score on the
final test was 73. This year the mean on the same final was 76.

Question 75

A psychologist claims that more than 5.8 percent of the population suffers from professional problems due to extreme shyness. Use p, the true percentage of the population that suffers from extreme shyness.

Question 76

Write the claim that is suggested by the given statement, then write a conclusion about the claim. Do not use
symbolic expressions or formal procedures; use common sense.
A person claims to have extra sensory powers. A card is drawn at random from a deck of cards and without
looking at the card, the person is asked to identify the suit of the card. He correctly identifies the suit 28 times
out of 100.

Question 77

Write the claim that is suggested by the given statement, then write a conclusion about the claim. Do not use
symbolic expressions or formal procedures; use common sense.
Of a group of 1000 people suffering from arthritis, 500 receive acupuncture treatment and 500 receive a placebo.
Among those in the placebo group, 24% noticed an improvement, while of those receiving acupuncture, 44%
noticed an improvement.

Question 78

What do you conclude about the claim below? Do not use formal procedures or exact calculations. Use only the
rare event rule and make a subjective estimate to determine whether the event is likely.
Claim: A company claims that the proportion of defective units among a particular model of computers is 4%.
In a shipment of 200 such computers, there are 10 defective units.

Question 79

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z
value used to test a null hypothesis.

Question 80

What do you conclude about the claim below? Do not use formal procedures or exact calculations. Use only the
rare event rule and make a subjective estimate to determine whether the event is likely.
Claim: A roulette wheel is fair and in 40 consecutive spins of the wheel, black shows up 23 times. (A roulette
wheel has 38 equally likely slots of which 18 are black).