Deck 8: Hypothesis Testing With Two Samples

Question 1

Find the standardized test statistic to test the claim that $\mu _ { 1 } < \mu _ { 2 }$ Assume the two samples are random and independent.
Population statistics: $\sigma _ { 1 } = 2.9 \text { and } \sigma _ { 2 } = 2.8$ Sample statisticsstatistics: $\overline { \mathrm { x } } 1 = 20.16 , \mathrm { n } _ { 1 } = 35 \text { and } \overline { \mathrm { x } } 2 = 22.71 , \mathrm { n } _ { 2 } = 42$

A)-3.90
B)-3.16
C)-2.63
D)-1.66

Answer 1

-3.90

Question 2

Suppose you want to test the claim that $\mu _ { 1 } > \mu _ { 2 }$ Assume the two samples are random and independent. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

A)There is sufficient evidence to support the claim μ $\mu _ { 1 } > \mu _ { 2 }$
B)There is sufficient evidence to reject the claim μ $\mu _ { 1 } > \mu _ { 2 }$
C)There is not sufficient evidence to reject the claim μ $\mu _ { 1 } > \mu _ { 2 }$
D)There is not sufficient evidence to support the claim μ $\mu _ { 1 } > \mu _ { 2 }$

Answer 2

There is sufficient evidence to support the claim μ $\mu _ { 1 } > \mu _ { 2 }$

Question 3

Classify the two given samples as independent or dependent. Sample 1: The scores of 22 students who took the ACT
Sample 2: The scores of 22 different students who took the SAT

A)independent
B)dependent

Answer 3

independent

Question 4

Classify the two given samples as independent or dependent. Sample 1: The weights in pounds of 21 newborn females
Sample 2: The weights in pounds of 21 newborn males

A)independent
B)dependent

Question 5

Suppose you want to test the claim that $\mu _ { 1 } \neq \mu _ { 2 }$ Assume the two samples are random and independent. At a level of significance of α = 0.02, when should you reject H₀?
Population statistics: $\sigma _ { 1 } = 0.76 \text { and } \sigma _ { 2 } = 0.51$ Sample statisticsstatistics: $\overline { \mathrm { x } } 1 = 1.8 , \mathrm { n } _ { 1 } = 51 \text { and } \overline { \mathrm { x } } 2 = 2.2 , \mathrm { n } _ { 2 } = 38$

A)Reject H₀ if the standardized test statistic is less than -2.33 or greater than 2.33.
B)Reject H₀ if the standardized test statistic is less than -1.96 or greater than 1.96.
C)Reject H₀ if the standardized test statistic is less than -1.645 or greater than 1.645.
D)Reject H₀ if the standardized test statistic is less than -2.575 or greater than 2.575.

Question 6

Find the standardized test statistic to test the claim that $\mu _ { 1 } = \mu _ { 2 } .$ Assume the two samples are random and independent.
Population statistics: $\sigma _ { 1 } = 1.5 \text { and } \sigma _ { 2 } = 1.9$ Sample statisticsstatistics: $\bar { x }_ 1 = 24 , \mathrm { n } _ { 1 } = 50 \text { and } \bar { x }_ 2 = 22 , n _ { 2 } = 60$

A)6.2
B)8.1
C)4.2
D)3.8

Question 7

As part of a Masterʹs thesis project, a mathematics teacher is interested in the effects of two different teaching methods on mathematics achievement. She randomly chooses one class of students to learn an algebraic
Concept using traditional methods and another class of students to learn the same algebraic concept using
Manipulatives. The teacher then compares their test scores. Determine whether the samples are dependent or
Independent.

A)independent
B)dependent

Question 8

Suppose you want to test the claim that $\mu _ { 1 } > \mu _ { 2 }$ AssumAssume the two samples are random and independent. At a level of significance of α = 0.01, when should you reject H₀?
Population statistics: $\sigma _ { 1 } = 45 \text { and } \sigma _ { 2 } = 25$ Sample statistics: $\overline { \mathrm { x } } 1 = 805 , \mathrm { n } _ { 1 } = 100 \text { and } \overline { \mathrm { x } } 2 = 790 , \mathrm { n } _ { 2 } = 125$

A)Reject H₀ if the standardized test statistic is greater than 2.33.
B)Reject H₀ if the standardized test statistic is greater than 1.96.
C)Reject H₀ if the standardized test statistic is greater than 1.645.
D)Reject H₀ if the standardized test statistic is greater than 2.575.

Question 9

Find the standardized test statistic to test the claim that $\mu _ { 1 } = \mu _ { 2 }$ . Assume the two samples are random and independent.
Population statistics: $\sigma _ { 1 } = 2.5 \text { and } \sigma _ { 2 } = 2.8$ Sample statistics: $\overline { \mathrm { x } } 1 = 3 , \mathrm { n } _ { 1 } = 40 \text { and } \overline { \mathrm { x } } 2 = 4 , \mathrm { n } _ { 2 } = 35$

A)-1.6
B)-0.8
C)-2.6
D)-1.0

Question 10

Find the standardized test statistic to test the claim that $\mu _ { 1 } \neq \mu _ { 2 } .$ Assume the two samples are random and independent.
Population statistics: $\sigma _ { 1 } = 0.76 \text { and } \sigma _ { 2 } = 0.51$ Sample statistics: $\overline { \mathrm { x } } 1 = 4.1 , \mathrm { n } _ { 1 } = 51 \text { and } \overline { \mathrm { x } } 2 = 4.5 , \mathrm { n } _ { 2 } = 38$

A)-2.97
B)-1.82
C)-2.12
D)-2.32

Question 11

Suppose you want to test the claim that $\mu _ { 1 } = \mu _ { 2 } .$ Assume the two samples are random and independent. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

A)There is sufficient evidence to reject the claim μ $\mu _ { 1 } = \mu _ { 2 } .$
B)There is not sufficient evidence to reject the claim μ $\mu _ { 1 } = \mu _ { 2 } .$
C)There is sufficient evidence to support the claim μ $\mu _ { 1 } = \mu _ { 2 }$
D)There is not sufficient evidence to support the claim μ $\mu _ { 1 } = \mu _ { 2 }$

Question 12

Suppose you want to test the claim that $\mu _ { 1 } \neq \mu _ { 2 } .$ Assume the two samples are random and independent. At a level of significance of α $\alpha$ = 0.05, when should you reject H₀?
Population statistics: $\sigma _ { 1 } = 1.5 \text { and } \sigma _ { 2 } = 1.9$ Sample statistics: $\overline { \mathrm { x } } 1 = 19 , \mathrm { n } _ { 1 } = 50 \text { and } \overline { \mathrm { x } } 2 = 17 , \mathrm { n } _ { 2 } = 60$

A)Reject H₀ if the standardized test statistic is less than -1.96 or greater than 1.96.
B)Reject H₀ if the standardized test statistic is less than -2.33 or greater than 2.33.
C)Reject H₀ if the standardized test statistic is less than -1.645 or greater than 1.645.
D)Reject H₀ if the standardized test statistic is less than -2.575 or greater than 2.575.

Question 13

Test the claim that Assume the two samples are random and independent. Use = 0.05.
Population statistics: Sample statisticsstatistics:

Question 14

Classify the two given samples as independent or dependent. Sample 1: Pre-training weights of 18 people
Sample 2: Post-training weights of 18 people

A)dependent
B)independent

Question 15

Suppose you want to test the claim that $\mu _ { 1 } < \mu _ { 2 }$ Assume the two samples are random and independent. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

A)There is not sufficient evidence to support the claim μ $\mu _ { 1 } < \mu _ { 2 }$
B)There is sufficient evidence to reject the claim μ $\mu _ { 1 } < \mu _ { 2 } .$
C)There is not sufficient evidence to reject the claim μ $\mu _ { 1 } < \mu _ { 2 }$ .
D)There is sufficient evidence to support the claim μ $\mu _ { 1 } < \mu _ { 2 }$

Question 16

As part of a marketing experiment, a department store regularly mailed discount coupons to 25 of its credit card holders. Their total credit card purchases over the next three months were compared to their prior credit
Card purchases during the previous three months. Determine whether the samples are dependent or
Independent.

A)dependent
B)independent

Question 17

Suppose you want to test the claim that $\mu _ { 1 } < \mu _ { 2 }$ Assume the two samples are random and independent. At a level of significance of α $\alpha$ = 0.05, when should you reject H₀?
Population statistics: $\sigma _ { 1 } = 2.9 \text { and } \sigma _ { 2 } = 2.8$ Sample statistics: $\overline { \mathrm { x } } 1 = 28.85 , \mathrm { n } _ { 1 } = 35 \text { and } \overline { \mathrm { x } } 2 = 31.4 , \mathrm { n } _ { 2 } = 42$

A)Reject H₀ if the standardized test statistic is less than -1.645.
B)Reject H₀ if the standardized test statistic is less than -1.96.
C)Reject H₀ if the standardized test statistic is less than -2.33.
D)Reject H₀ if the standardized test statistic is less than -2.575.

Question 18

Find the standardized test statistic to test the claim that $\mu _ { 1 } > \mu _ { 2 } .$ Assume the two samples are random and independent.
Population statistics: $\sigma _ { 1 } = 45 \text { and } \sigma _ { 2 } = 25$ Sample statistics: $\bar { x } 1 = 480 , n _ { 1 } = 100 \text { and } \bar { x } { 2 } = 465 , n _ { 2 } = 125$

A)2.99
B)2.81
C)1.86
D)0.91

Question 19

As part of a marketing experiment, a department store regularly mailed discount coupons to 25 of its credit card holders. Their total credit card purchases over the next three months were compared to the credit card
Purchases over the next three months for 25 credit card holders who were not sent discount coupons.
Determine whether the samples are dependent or independent.

A)independent
B)dependent

Question 20

As part of a Masterʹs thesis project, a mathematics teacher is interested in the effects of two different teaching methods on mathematics achievement. She randomly chooses a class of students to learn one algebraic concept
Using traditional methods. Then on another day, the same students learn a similar algebraic concept using
Manipulatives. The teacher then compares their test scores. Determine whether the samples are dependent or
Independent.

A)dependent
B)independent

Question 21

Test the claim that Assume the two samples are random and independent. Use Population statistics: Sample statisticsstatistics:

Question 22

A recent study of 100 elementary school teachers in a southern state found that their mean salary was $24,700
with a population standard deviation of $2100. A similar study of 100 elementary school teachers in a western
state found that their mean salary was $35,100 with a population standard deviation of $3200. Test the claim
that the salaries of elementary school teachers in the western state is more than $10,000 greater than that of
elementary teachers in the southern state. Use = 0.05. Assume the two samples are random and independent.

Question 23

At α = 0.05, test a financial advisorʹs claim that the difference between the mean dividend rate for listings in the
NYSE market and the mean dividend rate for listings in the NASDAQ market is more than 0.75. Assume the
two samples are random and independent.

Question 24

Suppose you want to test the claim that $\mu _ { 1 } \neq \mu _ { 2 }$ Assume the two samples are random and independent. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

A)There is not sufficient evidence to support the claim μ $\mu _ { 1 } \neq \mu _ { 2 } .$
B)There is sufficient evidence to reject the claim μ $\mu _ { 1 } \neq \mu _ { 2 }$
C)There is not sufficient evidence to reject the claim μ $\mu _ { 1 } \neq \mu _ { 2 }$
D)There is sufficient evidence to support the claim μ $\mu _ { 1 } \neq \mu _ { 2 }$

Question 25

A financial advisor wants to know whether there is a significant difference between the NYSE and NASDAQ
markets in the annual dividend rates for preferred stocks. A sample of 30 returns is selected from each market.
Assume the two samples are random and independent. Test the claim that there is no difference in the annual
dividend rates for the two markets. Use = 0.05.

Question 26

Two groups of patients with colorectal cancer are treated with a different drug to reduce pain. A random
sample of 140 patients are treated using the drug Irinotican and a random sample of 127 patients are treated
using the drug Fluorouracil. Assume the two samples are random and independent. At α = 0.01, test a
pharmaceutical representativeʹs claim that the difference between the mean number of pain-free months for
patients using Fluorouracil and the mean number of pain-free months for patients using Irinotican is less than
two months.

Question 27

A medical researcher suspects that the pulse rate of smokers is higher than the pulse rate of non-smokers. Test
the researcherʹs suspicion using α = 0.05. Assume the two samples are random and independent.

Question 28

A statistics teacher believes that students in an evening statistics class score higher than the students in a day
class. The results of a special exam are shown below. Assume the two samples are random and independent.
Can the teacher conclude that the evening students have a higher score? Use

Question 29

A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor
bank checks the waiting times at both banks. Use P-values to test the local bankʹs claim. Use = 0.05. Assume
the two samples are random and independent.

Question 30

Test the claim that Assume the two samples are random and independent. Use Population statistics: Sample statistics:

Question 31

Two samples are random and independent. Find the P-value used to test the claim that $\mu _ { 1 } > \mu _ { 2 } . \text { Use } \alpha = 0.05 \text {. }$ Population statistics: $\sigma _ { 1 } = 40 \text { and } \sigma _ { 2 } = 24$ Sample statistics: $\overline { \mathrm { x } } 1 = 615 , \mathrm { n } _ { 1 } = 100 \text { and } \bar { x } _ { 2 } = 600 , \mathrm { n } _ { 2 } = 125$

A)0.0005
B)0.0505
C)0.1015
D)0.5105

Question 32

A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor
bank checks the waiting times at both banks. Assume the two samples are random and independent. Use α = 0.05 and a confidence interval to test the local bankʹs claim.

Question 33

Two samples are random and independent. Find the P-value used to test the claim that $\mu _ { 1 } = \mu _ { 2 } \text {. Use } \alpha = 0.05 \text {. }$ Population statistics: $\sigma _ { 1 } = 2.5 \text { and } \sigma _ { 2 } = 2.8$ Sample statisticsstatistics: $\overline { \mathrm { x } } 1 = 12 , \mathrm { n } _ { 1 } = 40 \text { and } \overline { \mathrm { x } } 2 = 13 , \mathrm { n } _ { 2 } = 35$

A)0.1052
B)0.0526
C)0.4020
D)0.1138

Question 34

A study was conducted to determine if the salaries of elementary school teachers from two neighboring states
were equal. A sample of 100 teachers from each state was randomly selected. The mean from the first state was
$29,100 with a population standard deviation of $2300. The mean from the second state was $30,500 with a
population standard deviation of $2100. Test the claim that the salaries from both states are equal. Use

Question 35

A statistics teacher wanted to see whether there was a significant difference in ages between day students and
night students. A sample of 35 students is selected from each group. The data are given below. Assume the two
samples are random and independent. Test the claim that there is no difference in age between the two groups.
Use α Day Students Evening Students

Question 36

Construct a 95% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ Assume the two samples are random and independent. The sample statistics are given below.
Population statistics: $\sigma _ { 1 } = 1.5 \text { and } \sigma _ { 2 } = 1.9$ Sample statistics: $\overline { \mathrm { x } } 1 = 25 , \mathrm { n } _ { 1 } = 50 \text { and } \overline { \mathrm { x } } 2 = 23 , \mathrm { n } _ { 2 } = 60$

A)(1.364, 2.636)
B)(1.572, 2.987)
C)(1.723, 3.012)
D)(1.919, 3.142)

Question 37

Test the claim thathat Assume the two samples are random and independent. Use Population statistics: Sample statistics:

Question 38

At a local college, 65 female students were randomly selected and it was found that their mean monthly income
was $616 with a population standard deviation of $121.50. Seventy-five male students were also randomly
selected and their mean monthly income was found to be $658 with a population standard deviation of $168.70.
Test the claim that male students have a higher monthly income than female students. Use

Question 39

Construct a 95% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ Assume the two samples are random and independent. The sample statistics are given below.
Population statistics: $\sigma _ { 1 } = 2.5 \text { and } \sigma _ { 2 } = 2.8$ Sample statistics: $\overline { \mathrm { x } } 1 = 12 , \mathrm { n } _ { 1 } = 40 \text { and } \overline { \mathrm { x } } 2 = 13 , \mathrm { n } _ { 2 } = 35$

A)(-2.209, 0.209)
B)(-2.001, -1.873)
C)(-1.968, 1.561)
D)(-1.673, 1.892)

Question 40

A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor
bank checks the waiting times at both banks. Test the local bankʹs claim using α = 0.05. Assume the two
samples are random and independent.

Question 41

Suppose you want to test the claim that $\mu _ { 1 } = \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ At a
Level of significance of α $\alpha = 0.05$ when should you reject H₀? $$\begin{array} { l l } \mathrm { n } _ { 1 } = 14 & \mathrm { n } _ { 2 } = 12 \\\overline { \mathrm { x } } _ { 1 } = 21 & \overline { \mathrm { x } _ { 2 }} = 22 \\\mathrm {~s} _ { 1 } = 2.5 & \mathrm {~s} _ { 2 } = 2.8\end{array}$$

A)Reject H₀ if the standardized test statistic is less than -2.064 or greater than 2.064.
B)Reject H₀ if the standardized test statistic is less than -2.492 or greater than 2.492
C)Reject H₀ if the standardized test statistic is less than -1.711 or greater than 1.711.
D)Reject H₀ if the standardized test statistic is less than -1.318 or greater than 1.318.

Question 42

Find the standardized test statistic, t, to test the claim that $\mu _ { 1 } = \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 }^ { 2 } \text {. }$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 25 & \mathrm { n } _ { 2 } = 30 \\\overline { \mathrm { x } } 1 = 33 & \overline { \mathrm { x } } 2 = 31 \\\mathrm {~s} 1 = 1.5 & \mathrm {~s} _ { 2 } = 1.9\end{array}$$

A)4.361
B)3.287
C)2.892
D)1.986

Question 43

A researcher wishes to determine whether people with high blood pressure can lower their blood pressure by
following a certain diet. A treatment group and a control group are selected. Assume the two samples are
random and independent. Construct a 90% confidence interval for the difference between the two population
means, Would you recommend using this diet plan? Explain your reasoning.

Question 44

Suppose you want to test the claim that $\mu _ { 1 } = \mu _ { 2 }$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $$\sigma { } _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 }$$ At a
Level of significance of α $\alpha$ = 0.01, when should you reject H₀? $$\begin{array} { l l } \mathrm { n } _ { 1 } = 25 & \mathrm { n } _ { 2 } = 30 \\\overline { \mathrm { x } } 1 = 23 & \overline { \mathrm { x } } 2 = 21 \\\mathrm {~s} _ { 1 } = 1.5 & \mathrm {~s} _ { 2 } = 1.9\end{array}$$

A)Reject H₀ if the standardized test statistic is less than -2.797 or greater than 2.797.
B)Reject H₀ if the standardized test statistic is less than -2.789 or greater than 2.797.
C)Reject H₀ if the standardized test statistic is less than -1.711 or greater than 1.711.
D)Reject H₀ if the standardized test statistic is less than -2.492 or greater than 2.492.

Question 45

Find the standardized test statistic, t, to test the claim that $\mu _ { 1 } < \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 15 & \mathrm { n } _ { 2 } = 15 \\\overline { \mathrm { x } } 1 = 21.2 & \overline { \mathrm { x } } 2 = 23.75 \\\mathrm {~s} _ { 1 } = 2.9 & \mathrm {~s} _ { 2 } = 2.8\end{array}$$

A)-2.450
B)-3.165
C)-1.667
D)-0.669

Question 46

Suppose you want to test the claim that $\mu _ { 1 } < \mu _ { 2 }$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma _ { 1 } ^ { 2 } = \sigma _{ 2 } ^{ 2 } \text {. }$ At a
Level of significance of α $\alpha = 0.10 \text {, }$ when should you reject H₀? $$\begin{array} { l l } \mathrm { n } _ { 1 } = 15 & \mathrm { n } _ { 2 } = 15 \\\overline { \mathrm { x } }_ 1 = 27.37 & \overline { \mathrm { x } }_ 2 = 29.92 \\\mathrm {~s} _ { 1 } = 2.9 & \mathrm {~s}_ 2 = 2.8\end{array}$$

A)Reject H₀ if the standardized test statistic is less than -1.313.
B)Reject H₀ if the standardized test statistic is less than -2.467.
C)Reject H₀ if the standardized test statistic is less than -1.701.
D)Reject H₀ if the standardized test statistic is less than -0.683.

Question 47

Find the critical values, $\mathrm { t } _ { 0 } ,$ to test the claim that $\mu _ { 1 } = \mu 2$ Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that $\sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 } \text {. }$ Use $\alpha$ = 0.05. $$\begin{array} { l } \mathrm { n } _ { 1 } = 25 \\\overline { \mathrm { x } } 1 = 17 \\\mathrm {~s} _ { 1 } = 1.5\end{array}$$ $$\begin{array} { l } \mathrm { n } _ { 2 } = 30 \\\overline { \mathrm { x } _ { 2 } } = 15 \\\mathrm {~s} _ { 2 } = 1.9\end{array}$$

A) $\pm 2.064$
B) $\pm 2.797$
C) $\pm 1.711$
D)± $\pm 2.492$

Question 48

Test the claim that Two samples are random, independent, and come from populations that are
normally distributed. The sample statistics are given below. Assume that Use = 0.05.

Question 49

Suppose you want to test the claim that $\mu _ { 1 } \neq \mu _ { 2 }$ TTwo samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma \underset { 1 } { 2 } \neq \sigma _ { 2 } ^{ 2 }$ At a
Level of significance of α $\alpha$ = 0.20, when should you reject H₀? $$\begin{array} { l l } \mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \\\overline { \mathrm { x } }_ 1 = 2.9 & \overline { \mathrm { x } }_ 2 = 3.3 \\\mathrm {~s} _1 = 0.76 & \mathrm {~s}_ 2 = 0.51\end{array}$$

A)Reject H₀ if the standardized test statistic is less than -1.372 or greater than 1.372.
B)Reject H₀ if the standardized test statistic is less than -0.684 or greater than 0.684.
C)Reject H₀ if the standardized test statistic is less than -2.228 or greater than 2.228.
D)Reject H₀ if the standardized test statistic is less than -3.169 or greater than 3.169.

Question 50

Find the critical valuevalue, $t _ { 0 }$ to test the claim that $\mu _ { 1 } < \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that $$\sigma { } _ { 1 } ^ { 2 } = \sigma _ { 2 } ^{ 2 } \text {. Use } \alpha = 0.05$$ $$\begin{array} { l } \mathrm { n } _ { 1 } = 15 \\\overline { \mathrm { x } } _ { 1 } = 22.2 \\\mathrm {~s} _ { 1 } = 2.9\end{array}$$ $$\begin{array} { l } \mathrm { n } _ { 2 } = 15 \\\overline { \mathrm { x } _ { 2 } } = 24.75 \\\mathrm {~s} _ { 2 } = 2.8\end{array}$$

A)-1.701
B)2.467
C)-1.313
D)0.683

Question 51

Test the claim that Two samples are random, independent, and come from populations that are
normally distributed. The sample statistics are given below. Assume that

Question 52

Test the claim that Two samples are random, independent, and come from populations that are
normally distributed. The sample statistics are given below. Assume that . Use = 0.01.

Question 53

For which confidence interval for the difference in the means $\mu _ { 1 } - \mu _ { 2 } ,$ would you reject the null hypothesis?

A)(-2.001, -1.873)
B)(-1.968, 1.561)
C)(-1.673, 1.892)
D)(-2.209, 0.209)

Question 54

Suppose you want to test the claim that $\mu _ { 1 } > \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma { } _ { 1 } ^ { 2 } \neq \sigma_ { 2 } ^{ 2 }$ At a
Level of significance of α $\alpha$ = 0.01, when should you reject H₀? $$\begin{array} { l l } \mathrm { n } _ { 1 } = 18 & \mathrm { n } _ { 2 } = 13 \\\overline { \mathrm { x } }_ 1 = 595 & \overline { \mathrm { x } }_ 2 = 580 \\\mathrm {~s} 1 = 40 & \mathrm {~s} 2 = 25\end{array}$$

A)Reject H₀ if the standardized test statistic is greater than 2.681.
B)Reject H₀ if the standardized test statistic is greater than 1.699.
C)Reject H₀ if the standardized test statistic is greater than 2.179.
D)Reject H₀ if the standardized test statistic is greater than 3.055.

Question 55

Find the standardized test statistic, t, to test the claim that $\mu _ { 1 } = \mu _ { 2 }$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 14 & \mathrm { n } _ { 2 } = 12 \\\overline { \mathrm { x } _ { 1 } } = 14 & \overline { \mathrm { x } 2 } = 15 \\\mathrm {~s} _ { 1 } = 2.5 & \mathrm {~s} _ { 2 } = 2.8\end{array}$$

A)-0.962
B)-0.813
C)-1.326
D)-1.101

Question 56

Find the standardized test statistic, t, to test the claim that $\mu _ { 1 } > \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma \stackrel { 2 } { 1 } \neq \sigma _ { 2 } ^{ 2 }$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 18 & \mathrm { n } _ { 2 } = 13 \\\overline { \mathrm { x } } 1 = 515 & \overline { \mathrm { x } _ { 2 } } = 500 \\\mathrm {~s} _ { 1 } = 40 & \mathrm {~s} _ { 2 } = 25\end{array}$$

A)1.282
B)3.271
C)2.819
D)1.865

Question 57

Find the critical values, $\mathrm { t } _ { 0 }$ to test the claim that $\mu _ { 1 } = \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ Use $\alpha$ = 0.05. $$\begin{array} { l l } \mathrm { n } _ { 1 } = 14 & \mathrm { n } _ { 2 } = 12 \\\overline { \mathrm { x } } 1 = 15 & \overline { \mathrm { x } } 2 = 16 \\\mathrm {~s} _ { 1 } = 2.5 & \mathrm {~s} _ { 2 } = 2.8\end{array}$$

A) $\pm 2.064$
B) $\pm 2.492$
C) $\pm 1.711$
D) $\pm 1.318$

Question 58

Find the critical value, $t _ { 0 }$ to test the claim that $\mu _ { 1 } \neq \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that $\sigma \sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^{ 2 } \text {. Use } \alpha = 0.02$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \\\overline { \mathrm { x } } 1 = 3.9 & \overline { \mathrm { x } _ { 2 } } = 4.3 \\\mathrm {~s} _ { 1 } = 0.76 & \mathrm {~s} _ { 2 } = 0.51\end{array}$$

A) $\pm 2.764$
B) $\pm 0.684$
C) $\pm 2.228$
D) $\pm 3.169$

Question 59

Find the critical value, $t _ { 0 }$ to test the claim that $\mu _ { 1 } > \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that $\sigma { } _ { 1 } ^ { 2 } \neq \sigma _ { 2 }^ { 2 }$ Use α = 0.01. $$\begin{array} { l l } \mathrm { n } _ { 1 } = 18 & \mathrm { n } _ { 2 } = 13 \\\overline { \mathrm { x } } 1 = 600 & \overline { \mathrm { x } _ { 2 } } = 585 \\\mathrm {~s} _ { 1 } = 40 & \mathrm {~s} _ { 2 } = 25\end{array}$$

A)2.681
B)1.699
C)2.179
D)3.055

Question 60

Find the standardized test statistic, t, to test the claim that $\mu _ { 1 } \neq \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma \sigma _ { 1 } ^ { 2 } \neq \sigma _{ 2 }^ { 2 } .$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \\\overline { \mathrm { x } } 1 = 6.9 & \overline { \mathrm { x } } 2 = 7.3 \\\mathrm {~s} _ { 1 } = 0.76 & \mathrm {~s} _ { 2 } = 0.51\end{array}$$

A)-1.546
B)-1.821
C)-2.123
D)-1.326

Question 61

Construct a 90% confidence interval for $\mu _ { 1 } - \mu _ { 2 } .$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $$\sigma _ { 1 } ^ { 2 } = \sigma { } _ { 2 } ^ { 2 }$$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 10 & \mathrm { n } _ { 2 } = 12 \\\overline { \mathrm { x } } 1 = 25 & \overline { \mathrm { x } } 2 = 23 \\\mathrm {~s} _ { 1 } = 1.5 & \mathrm {~s} _ { 2 } = 1.9\end{array}$$

A)(0.721, 3.279)
B)(1.335, 3.012)
C)(1.413, 3.124)
D)(1.554, 3.651)

Question 62

A womenʹs advocacy group claims that women golfers receive significantly less prize money than their male
counterparts when they win first place in a professional tournament. The data listed below are the first place
prize monies from male and female tournament winners. Assume the samples are random, independent, and
come from populations that are normally distributed. At α = 0.01, test the groupʹs claim. Assume the
population variances are not equal.

Question 63

Find $\overline { \mathrm { d } } .$ Assume the samples are random and dependent, and the populations are normally distributed. $$\begin{array} { c | c c c c c } \mathrm { A } & 2.5 & 3.5 & 5.4 & 2.4 & 2.5 \\\hline \mathrm { B } & 4.9 & 3.8 & 3.7 & 3.6 & 5.0\end{array}$$

A)-0.94
B)-0.76
C)0.58
D)0.89

Question 64

Find $\overline { \mathrm { d } } .$ Assume the samples are random and dependent, and the populations are normally distributed. $$\begin{array} { c | c c c c c } \mathrm { A } & 13 & 11 & 30 & 26 & 14 \\\hline \mathrm { B } & 11 & 7 & 8 & 18 & 5\end{array}$$

A)9.0
B)-5.1
C)33.1
D)25.2

Question 65

Construct a 95% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ Two samples are random, independent, and come from populations that are normally distributed The sample statistics are given below. Assume that $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \\\overline { \mathrm { x } } 1 = 4.8 & \overline { \mathrm { x } } 2 = 5.2 \\\mathrm {~s} _ { 1 } = 0.76 & \mathrm {~s} _ { 2 } = 0.51\end{array}$$

A)(-0.883, 0.083)
B)(-4.152, 3.981)
C)(-2.762, 2.762)
D)(-1.762, 1.762)

Question 66

A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitorʹs
bank checks the waiting times at both banks. Assume the samples are random and independent, and the
populations are normally distributed. Test the local bankʹs claim: (a)assuming that assuming that

Question 67

A womenʹs advocacy group claims that women golfers receive significantly less prize money than their male
counterparts when they win first place in a professional tournament. The data listed below are the first place
prize monies from male and female tournament winners. Assume the samples are random, independent, and
come from populations that are normally distributed. Construct a 99% confidence interval for the difference in
the means Assume the population variances are not equal.

Question 68

Test the claim that Two samples are random, independent, and come from populations that are
normally distributed. The sample statistics are given below. Assume that

Question 69

Find the critical value, $t _ { 0 }$ to test the claim that $\mu _ { \mathrm { d } }$ = 0. Assume the samples are random and dependent, and the populations are normally distributed. Use $\alpha$ = 0.05. $$\begin{array} { c | l l l l l } \text { A } & 19 & 17 & 36 & 32 & 20 \\\hline \text { B } & 17 & 13 & 14 & 24 & 11\end{array}$$

A) $\pm 2.776$
B)2.132
C) $\pm 4.604$
D)3.747

Question 70

Find the critical value, $t _ { 0 } ,$ to test the claim that $\mu _ { \mathrm { d } }$ = 0. Assume the samples are random and dependent, and the populations are normally distributed. Use $\alpha$ = 0.01. $$\begin{array} { r | r r r r r } \text { A } & 8.2 & 9.2 & 11.1 & 8.1 & 8.2 \\\hline \text { B } & 10.6 & 9.5 & 9.4 & 9.3 & 10.7\end{array}$$

A) $\pm 4.604$
B) $\pm 3.747$
C)2.132
D)0.741

Question 71

A study was conducted to determine if the salaries of elementary school teachers from two neighboring
districts were equal. A sample of 15 teachers from each district was randomly selected. The mean from the first
district was $28,900 with a standard deviation of $2300. The mean from the second district was $30,300 with a
standard deviation of $2100. Test the claim that the salaries from both districts are equal. Assume the samples
are random and independent, and the populations are normally distributed. Also, assume that Use

Question 72

A study was conducted to determine if the salaries of elementary school teachers from two neighboring districts were equal. A sample of 15 teachers from each district was randomly selected. The mean from the first
District was $28,900 with a standard deviation of $2300. The mean from the second district was $30,300 with a
Standard deviation of $2100. Assume the samples are random, independent, and come from populations that
Are normally distributed. Construct a 95% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ Assume that $\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 } \text {. }$

A)(-3047, 247)
B)(-2054, 238)
C)(-2871, 567)
D)(-4081, 597)

Question 73

Test the claim that the paired sample data is from a population with a mean difference of 0. Assume the
samples are random and dependent, and the populations are normally distributed. Use

Question 74

Find $\mathrm { s } _ { \mathrm { d } }$ Assume the samples are random and dependent, and the populations are normally distributed. $$\begin{array} { c | c c c c c } \text { A } & 5.3 & 6.3 & 8.2 & 5.2 & 5.3 \\\hline \text { B } & 7.7 & 6.6 & 6.5 & 6.4 & 7.8\end{array}$$

A)1.73
B)1.21
C)1.32
D)1.89

Question 75

Find the critical value, $t _ { 0 }$ to test the claim that $\mu _ { \mathrm { d } }$ = 0. Assume the samples are random and dependent, and the populations are normally distributed. Use $\alpha$ = 0.02. $$\begin{array} { c | c c c c c } \mathrm { A } & 8 & 9.2 & 11.1 & 8.1 & 8.2 \\\hline \text { B } & 5.4 & 4.3 & 5.2 & 4.1 & 5.5\end{array}$$

A) $\pm 3.747$
B) $\pm 4.604$
C)2.132
D)0.741

Question 76

A sports analyst claims that the mean batting average for teams in the American League is not equal to the
mean batting average for teams in the National League because a pitcher does not bat in the American League.
The data listed below are random, independent, and come from populations that are normally distributed. At α = 0.05, test the sports analystʹs claim. Assume the population variances are equal.

Question 77

A sports analyst claims that the mean batting average for teams in the American League is not equal to the
mean batting average for teams in the National League because a pitcher does not bat in the American League.
The data listed below are random, independent, and come from populations that are normally distributed.
Construct a 95% confidence interval for the difference in the means Assume the population variances
are equal.

Question 78

Find $\mathrm { s } _ { \mathrm { d } }$ Assume the samples are random and dependent, and the populations are normally distributed. $$\begin{array} { c | l l l l l } \text { A } & 27 & 25 & 44 & 40 & 28 \\\hline \text { B } & 25 & 21 & 22 & 32 & 19\end{array}$$

A)7.8
B)5.6
C)6.8
D)8.9

Question 79

Test the claim that Two samples are random, independent, and come from populations that are
normally distributed. The sample statistics are given below. Assume that

Question 80

Construct a 95% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below. Assume that $\sigma \underset { 1 } { 2 } = \sigma _{ 2 } ^{ 2 }$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 8 & \mathrm { n } _ { 2 } = 7 \\\overline { \mathrm { x } } 1 = 4.1 & \overline { \mathrm { x } } 2 = 5.5 \\\mathrm {~s} _ { 1 } = 0.76 & \mathrm {~s} _ { 2 } = 2.51\end{array}$$

A)(-3.406, 0.606)
B)(-1.132, 1.543)
C)(-1.679, 1.987)
D)(2.112, 2.113)