Question 1

Given the following information about a hypothesis test of the difference between two means based on independent random samples,what is the standard deviation of the difference between the two means? Assume that the samples are obtained from normally distributed populations having equal variances. H_A: ?_A > ?_B, $\bar { X } _ { 1 } = 12$ $\bar { X } _ { 2 } = 9$ S₁ = 5,s₂ = 3,n₁ = 13,n₂ = 10. A)1.792 B)1.679 C)2.823 D)3.210 E)1.478

Accepted Answer

The standard deviation of the difference between the two means is:$$\sigma_{\bar{X}_1 - \bar{X}_2} = \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}$$Since the samples are obtained from normally distributed populations having equal variances, we can use the pooled variance to estimate the common variance:$$s_p^2 = \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1 + n_2 - 2}$$$$s_p^2 = \frac{(13-1)(5)^2 + (10-1)(3)^2}{13 + 10 - 2} = 16.2$$Therefore, the standard deviation of the difference between the two means is:$$\sigma_{\bar{X}_1 - \bar{X}_2} = \sqrt{\frac{16.2}{13} + \frac{16.2}{10}} = 1.792$$

Question 2

When we test H₀: μ₁ ≤ μ₂,H_A: μ₁ > μ₂ at α = .10,where $\bar { X } _ { 1 }$ = 77.4, $\bar { X } _ { 2 }$ = 72.2,s₁ = 3.3,s₂ = 2.1,n₁ = 6,n₂ = 6,what is the estimated pooled variance?

Accepted Answer

The answer of When we test H₀: μ₁ ≤ μ₂,H_A:...

Question 3

Using a 90 percent confidence interval for the difference between the proportions of failures in factory 1 and factory 2,where $\hat { p } _ { 1 }$ = .05, $\hat { p } _ { 2 }$ = .04,n₁ = 500,n₂ = 2000 of [-.0076,.0276],can we reject the null hypothesis at α = .10?

Accepted Answer

The answer of Using a 90 percent confidence interval for...

Question 4

Find a 95 percent confidence interval for μ₁ - μ₂,where n₁ = 15,n₂ = 10,$\bar { X } _ { 1 }$ = 1.94, $\bar { X } _ { 2 }$ = 1.04,s₁² = .2025 and s₂² = .0676.(Assume equal population variances. )

Accepted Answer

The answer of Find a 95 percent confidence interval for...

Question 5

The test of means for two related populations matches the observations (matched pairs)in order to reduce the ________________ attributable to the difference between individual observations and other factors.
A)Means
B)Test statistic
C)Degrees of freedom
D)Variation

Accepted Answer

By using matched pairs, we are able to reduce the variation attributable to factors that may be different between the two populations (e.g. age, gender, location, etc.). Therefore, option D is the correct answer.

Question 6

Construct a 95 percent confidence interval for μ₁ - μ₂,where $\bar { X } _ { 1 }$ = 34.36, $\bar { X } _ { 2 }$ = 26.45,s₁ = 9,s₂ = 6,n₁ = 10,n₂ = 16.(Assume equal population variances. )

Accepted Answer

The answer of Construct a 95 percent confidence interval for...

Question 7

Find a 95 percent confidence interval for μ₁ - μ₂,where n₁ = 50,n₂ = 75, $\bar { X } _ { 1 }$ = 82, $\bar { X } _ { 2 }$ = 76,s₁² = 8,and s₂² = 6.Assume unequal variances.

Accepted Answer

The answer of Find a 95 percent confidence interval for...

Question 8

When we test H₀: μ₁ ≤ μ₂,H_A: μ₁ > μ₂ at α = .10,where $\bar { X } _ { 1 }$ = 77.4, $\bar { X } _ { 2 }$ = 72.2,s₁ = 3.3,s₂ = 2.1,n₁ = 6,n₂ = 6,can we reject the null hypothesis?

Accepted Answer

The answer of When we test H₀: μ₁ ≤ μ₂,H_A:...

Question 9

Find a 95 percent confidence interval for the difference between means,where n₁ = 50,n₂ = 36, $\bar { X } _ { 1 }$ = 80, $\bar { X } _ { 2 }$ = 75,s₁² = 5,and s₂² = 3.Assume unequal variances.

Accepted Answer

The answer of Find a 95 percent confidence interval for...

Question 10

Given two independent normal distributions with s₁² - s₂² = 100,?₁ = ?₂ = 50,n₁ = n₂ = 50,the sampling distribution of the mean difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ Will have a mean of _________. A)1 B)0 C)50 D)100

Accepted Answer

The mean of the sampling distribution of the mean difference will be equal to the difference in the population means, which is μ₁ - μ₂ = 0. Therefore, the answer is B.

Question 11

When we test H₀: p₁ - p₂ ≤ .01,H_A: p₁ - p₂ > .01 at α = .05 where $\hat { p } _ { 1 }$ = .08, $\hat { p } _ { 2 }$ = .035,n₁ = 200,n₂ = 400,can we reject the null hypothesis?

Accepted Answer

The answer of When we test H₀: p₁ - p₂...

Question 12

When testing H₀: μ₁ - μ₂ = 2,H_A: μ₁ - μ₂ > 2,where $\bar { X } _ { 1 }$ = 522, $\bar { X }_ { 2}$ = 516,s₁² = 28,s₂² = 24,n₁ = 40,n₂ = 30,at α = .01,what can we conclude?

Accepted Answer

The answer of When testing H₀: μ₁ - μ₂ =...

Question 13

Given the following information about a hypothesis test of the difference between two means based on independent random samples,what is the calculated value of the test statistic? Assume that the samples are obtained from normally distributed populations having equal variances. H_A: ?_A > ?_B, $\bar { Y } _ { 1 } = 12$ $\bar { X } _ { 2 } = 9$ S₁ = 5,s₂ = 3,n₁ = 13,n₂ = 10. A)t = 1.96 B)t = 1.5 C)t = 2.823 D)t = 1.674 E)t = 1.063

Accepted Answer

The answer of Given the following information about a hypothesis...

Question 14

Find a 90 percent confidence interval for the difference between the proportions of failures in factory 1 and factory 2,where $\hat { p } _ { 1 }$ = .05, $\hat { p } _ { 2 }$ = .04,n₁ = 500,n₂ = 2000.

Accepted Answer

The answer of Find a 90 percent confidence interval for...

Question 15

Find a 95 percent confidence interval for the difference between the proportions of older and younger drivers who have tickets,where $\hat { p } _ { 1 }$ = .275, $\hat { p } _ { 2 }$ = .25,n₁ = 1000,n₂ = 1000.

Accepted Answer

The answer of Find a 95 percent confidence interval for...

Question 16

If we are testing the hypothesis about the mean of a population of paired differences with samples of n₁ = 8,n₂ = 8,the degrees of freedom for the t statistic is ____. A)16 B)7 C)14 D)9

Accepted Answer

Paired differences degrees of freedom = n − 1 = 8 − 1 = 7

Question 17

In testing the difference between the means of two normally distributed populations,if μ₁ = μ₂ = 50,n₁ = 9,n₂ = 13,the degrees of freedom for the t statistic equals ___________. A)22 B)21 C)19 D)20

Accepted Answer

The answer of In testing the difference between the means...

Question 18

When we test H₀: p₁ - p₂ ≤ .01,H_A: p₁ - p₂ > .01,at α = .05,where $\hat { p } _ { 1 }$ = .08, $\hat { p } _ { 2 }$ = .035,n₁ = 200,and n₂ = 400,what is the standard deviation used in the calculation of the test statistic?

Accepted Answer

The answer of When we test H₀: p₁ - p₂...

Question 19

Find a 98 percent confidence interval for the paired difference. $d_{1}-d_{2} \text { where } \overline{\mathrm{D}}=1.6, s_{d}^{2}=40.96, n=30$

Accepted Answer

The answer of Find a 98 percent confidence interval for...

Question 20

When testing H₀: μ₁ - μ₂ = 2,H_A: μ₁ - μ₂ > 2,where $\bar { X } _ { 1 }$ = 522, $\bar { X } _ { 2 }$ = 516,σ₁² = 28,σ₂² = 24,n₁ = 40,n₂ = 30,at α = .01,what is the test statistic?

Accepted Answer

The answer of When testing H₀: μ₁ - μ₂ =...

Quiz 10: Comparing Two Means and Two Proportions

When we test H₀: μ₁ ≤ μ₂,H_A: μ₁ > μ₂ at α = .10,where $\bar { X } _ { 1 }$ = 77.4, $\bar { X } _ { 2 }$ = 72.2,s₁ = 3.3,s₂ = 2.1,n₁ = 6,n₂ = 6,what is the estimated pooled variance?

Using a 90 percent confidence interval for the difference between the proportions of failures in factory 1 and factory 2,where $\hat { p } _ { 1 }$ = .05, $\hat { p } _ { 2 }$ = .04,n₁ = 500,n₂ = 2000 of [-.0076,.0276],can we reject the null hypothesis at α = .10?

Find a 95 percent confidence interval for μ₁ - μ₂,where n₁ = 15,n₂ = 10, $\bar { X } _ { 1 }$ = 1.94, $\bar { X } _ { 2 }$ = 1.04,s₁² = .2025 and s₂² = .0676.(Assume equal population variances. )

The test of means for two related populations matches the observations (matched pairs) in order to reduce the ________________ attributable to the difference between individual observations and other factors.

Construct a 95 percent confidence interval for μ₁ - μ₂,where $\bar { X } _ { 1 }$ = 34.36, $\bar { X } _ { 2 }$ = 26.45,s₁ = 9,s₂ = 6,n₁ = 10,n₂ = 16.(Assume equal population variances. )

Find a 95 percent confidence interval for μ₁ - μ₂,where n₁ = 50,n₂ = 75, $\bar { X } _ { 1 }$ = 82, $\bar { X } _ { 2 }$ = 76,s₁² = 8,and s₂² = 6.Assume unequal variances.

When we test H₀: μ₁ ≤ μ₂,H_A: μ₁ > μ₂ at α = .10,where $\bar { X } _ { 1 }$ = 77.4, $\bar { X } _ { 2 }$ = 72.2,s₁ = 3.3,s₂ = 2.1,n₁ = 6,n₂ = 6,can we reject the null hypothesis?

Find a 95 percent confidence interval for the difference between means,where n₁ = 50,n₂ = 36, $\bar { X } _ { 1 }$ = 80, $\bar { X } _ { 2 }$ = 75,s₁² = 5,and s₂² = 3.Assume unequal variances.

Given two independent normal distributions with s₁² - s₂² = 100,?₁ = ?₂ = 50,n₁ = n₂ = 50,the sampling distribution of the mean difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ Will have a mean of _________.

When we test H₀: p₁ - p₂ ≤ .01,H_A: p₁ - p₂ > .01 at α = .05 where $\hat { p } _ { 1 }$ = .08, $\hat { p } _ { 2 }$ = .035,n₁ = 200,n₂ = 400,can we reject the null hypothesis?

When testing H₀: μ₁ - μ₂ = 2,H_A: μ₁ - μ₂ > 2,where $\bar { X } _ { 1 }$ = 522, $\bar { X }_ { 2}$ = 516,s₁² = 28,s₂² = 24,n₁ = 40,n₂ = 30,at α = .01,what can we conclude?

Find a 90 percent confidence interval for the difference between the proportions of failures in factory 1 and factory 2,where $\hat { p } _ { 1 }$ = .05, $\hat { p } _ { 2 }$ = .04,n₁ = 500,n₂ = 2000.

Find a 95 percent confidence interval for the difference between the proportions of older and younger drivers who have tickets,where $\hat { p } _ { 1 }$ = .275, $\hat { p } _ { 2 }$ = .25,n₁ = 1000,n₂ = 1000.

If we are testing the hypothesis about the mean of a population of paired differences with samples of n₁ = 8,n₂ = 8,the degrees of freedom for the t statistic is ____.

In testing the difference between the means of two normally distributed populations,if μ₁ = μ₂ = 50,n₁ = 9,n₂ = 13,the degrees of freedom for the t statistic equals ___________.

When we test H₀: p₁ - p₂ ≤ .01,H_A: p₁ - p₂ > .01,at α = .05,where $\hat { p } _ { 1 }$ = .08, $\hat { p } _ { 2 }$ = .035,n₁ = 200,and n₂ = 400,what is the standard deviation used in the calculation of the test statistic?

Find a 98 percent confidence interval for the paired difference. $d_{1}-d_{2} \text { where } \overline{\mathrm{D}}=1.6, s_{d}^{2}=40.96, n=30$

When testing H₀: μ₁ - μ₂ = 2,H_A: μ₁ - μ₂ > 2,where $\bar { X } _ { 1 }$ = 522, $\bar { X } _ { 2 }$ = 516,σ₁² = 28,σ₂² = 24,n₁ = 40,n₂ = 30,at α = .01,what is the test statistic?

Quiz 10: Comparing Two Means and Two Proportions

When we test H0: μ1 ≤ μ2,HA: μ1 > μ2 at α = .10,where Xˉ1\bar { X } _ { 1 }Xˉ1​ = 77.4, Xˉ2\bar { X } _ { 2 }Xˉ2​ = 72.2,s1 = 3.3,s2 = 2.1,n1 = 6,n2 = 6,what is the estimated pooled variance?

Using a 90 percent confidence interval for the difference between the proportions of failures in factory 1 and factory 2,where p^1\hat { p } _ { 1 }p^​1​ = .05, p^2\hat { p } _ { 2 }p^​2​ = .04,n1 = 500,n2 = 2000 of [-.0076,.0276],can we reject the null hypothesis at α = .10?

Find a 95 percent confidence interval for μ1 - μ2,where n1 = 15,n2 = 10, Xˉ1\bar { X } _ { 1 }Xˉ1​ = 1.94, Xˉ2\bar { X } _ { 2 }Xˉ2​ = 1.04,s12 = .2025 and s22 = .0676.(Assume equal population variances. )

The test of means for two related populations matches the observations (matched pairs) in order to reduce the ________________ attributable to the difference between individual observations and other factors.

Construct a 95 percent confidence interval for μ1 - μ2,where Xˉ1\bar { X } _ { 1 }Xˉ1​ = 34.36, Xˉ2\bar { X } _ { 2 }Xˉ2​ = 26.45,s1 = 9,s2 = 6,n1 = 10,n2 = 16.(Assume equal population variances. )

Find a 95 percent confidence interval for μ1 - μ2,where n1 = 50,n2 = 75, Xˉ1\bar { X } _ { 1 }Xˉ1​ = 82, Xˉ2\bar { X } _ { 2 }Xˉ2​ = 76,s12 = 8,and s22 = 6.Assume unequal variances.

When we test H0: μ1 ≤ μ2,HA: μ1 > μ2 at α = .10,where Xˉ1\bar { X } _ { 1 }Xˉ1​ = 77.4, Xˉ2\bar { X } _ { 2 }Xˉ2​ = 72.2,s1 = 3.3,s2 = 2.1,n1 = 6,n2 = 6,can we reject the null hypothesis?

Find a 95 percent confidence interval for the difference between means,where n1 = 50,n2 = 36, Xˉ1\bar { X } _ { 1 }Xˉ1​ = 80, Xˉ2\bar { X } _ { 2 }Xˉ2​ = 75,s12 = 5,and s22 = 3.Assume unequal variances.

Given two independent normal distributions with s12 - s22 = 100,?1 = ?2 = 50,n1 = n2 = 50,the sampling distribution of the mean difference Xˉ1−Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 }Xˉ1​−Xˉ2​ Will have a mean of _________.

When we test H0: p1 - p2 ≤ .01,HA: p1 - p2 > .01 at α = .05 where p^1\hat { p } _ { 1 }p^​1​ = .08, p^2\hat { p } _ { 2 }p^​2​ = .035,n1 = 200,n2 = 400,can we reject the null hypothesis?

When testing H0: μ1 - μ2 = 2,HA: μ1 - μ2 > 2,where Xˉ1\bar { X } _ { 1 }Xˉ1​ = 522, Xˉ2\bar { X }_ { 2}Xˉ2​ = 516,s12 = 28,s22 = 24,n1 = 40,n2 = 30,at α = .01,what can we conclude?

Find a 90 percent confidence interval for the difference between the proportions of failures in factory 1 and factory 2,where p^1\hat { p } _ { 1 }p^​1​ = .05, p^2\hat { p } _ { 2 }p^​2​ = .04,n1 = 500,n2 = 2000.

Find a 95 percent confidence interval for the difference between the proportions of older and younger drivers who have tickets,where p^1\hat { p } _ { 1 }p^​1​ = .275, p^2\hat { p } _ { 2 }p^​2​ = .25,n1 = 1000,n2 = 1000.

If we are testing the hypothesis about the mean of a population of paired differences with samples of n1 = 8,n2 = 8,the degrees of freedom for the t statistic is ____.

In testing the difference between the means of two normally distributed populations,if μ1 = μ2 = 50,n1 = 9,n2 = 13,the degrees of freedom for the t statistic equals ___________.

When we test H0: p1 - p2 ≤ .01,HA: p1 - p2 > .01,at α = .05,where p^1\hat { p } _ { 1 }p^​1​ = .08, p^2\hat { p } _ { 2 }p^​2​ = .035,n1 = 200,and n2 = 400,what is the standard deviation used in the calculation of the test statistic?

Find a 98 percent confidence interval for the paired difference. d1−d2 where D‾=1.6,sd2=40.96,n=30d_{1}-d_{2} \text { where } \overline{\mathrm{D}}=1.6, s_{d}^{2}=40.96, n=30d1​−d2​ where D=1.6,sd2​=40.96,n=30

When testing H0: μ1 - μ2 = 2,HA: μ1 - μ2 > 2,where Xˉ1\bar { X } _ { 1 }Xˉ1​ = 522, Xˉ2\bar { X } _ { 2 }Xˉ2​ = 516,σ12 = 28,σ22 = 24,n1 = 40,n2 = 30,at α = .01,what is the test statistic?

When we test H₀: μ₁ ≤ μ₂,H_A: μ₁ > μ₂ at α = .10,where $\bar { X } _ { 1 }$ = 77.4, $\bar { X } _ { 2 }$ = 72.2,s₁ = 3.3,s₂ = 2.1,n₁ = 6,n₂ = 6,what is the estimated pooled variance?

Using a 90 percent confidence interval for the difference between the proportions of failures in factory 1 and factory 2,where $\hat { p } _ { 1 }$ = .05, $\hat { p } _ { 2 }$ = .04,n₁ = 500,n₂ = 2000 of [-.0076,.0276],can we reject the null hypothesis at α = .10?

Find a 95 percent confidence interval for μ₁ - μ₂,where n₁ = 15,n₂ = 10, $\bar { X } _ { 1 }$ = 1.94, $\bar { X } _ { 2 }$ = 1.04,s₁² = .2025 and s₂² = .0676.(Assume equal population variances. )

Construct a 95 percent confidence interval for μ₁ - μ₂,where $\bar { X } _ { 1 }$ = 34.36, $\bar { X } _ { 2 }$ = 26.45,s₁ = 9,s₂ = 6,n₁ = 10,n₂ = 16.(Assume equal population variances. )

Find a 95 percent confidence interval for μ₁ - μ₂,where n₁ = 50,n₂ = 75, $\bar { X } _ { 1 }$ = 82, $\bar { X } _ { 2 }$ = 76,s₁² = 8,and s₂² = 6.Assume unequal variances.

When we test H₀: μ₁ ≤ μ₂,H_A: μ₁ > μ₂ at α = .10,where $\bar { X } _ { 1 }$ = 77.4, $\bar { X } _ { 2 }$ = 72.2,s₁ = 3.3,s₂ = 2.1,n₁ = 6,n₂ = 6,can we reject the null hypothesis?

Find a 95 percent confidence interval for the difference between means,where n₁ = 50,n₂ = 36, $\bar { X } _ { 1 }$ = 80, $\bar { X } _ { 2 }$ = 75,s₁² = 5,and s₂² = 3.Assume unequal variances.

Given two independent normal distributions with s₁² - s₂² = 100,?₁ = ?₂ = 50,n₁ = n₂ = 50,the sampling distribution of the mean difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ Will have a mean of _________.

When we test H₀: p₁ - p₂ ≤ .01,H_A: p₁ - p₂ > .01 at α = .05 where $\hat { p } _ { 1 }$ = .08, $\hat { p } _ { 2 }$ = .035,n₁ = 200,n₂ = 400,can we reject the null hypothesis?

When testing H₀: μ₁ - μ₂ = 2,H_A: μ₁ - μ₂ > 2,where $\bar { X } _ { 1 }$ = 522, $\bar { X }_ { 2}$ = 516,s₁² = 28,s₂² = 24,n₁ = 40,n₂ = 30,at α = .01,what can we conclude?

Find a 90 percent confidence interval for the difference between the proportions of failures in factory 1 and factory 2,where $\hat { p } _ { 1 }$ = .05, $\hat { p } _ { 2 }$ = .04,n₁ = 500,n₂ = 2000.

Find a 95 percent confidence interval for the difference between the proportions of older and younger drivers who have tickets,where $\hat { p } _ { 1 }$ = .275, $\hat { p } _ { 2 }$ = .25,n₁ = 1000,n₂ = 1000.

If we are testing the hypothesis about the mean of a population of paired differences with samples of n₁ = 8,n₂ = 8,the degrees of freedom for the t statistic is ____.

In testing the difference between the means of two normally distributed populations,if μ₁ = μ₂ = 50,n₁ = 9,n₂ = 13,the degrees of freedom for the t statistic equals ___________.

When we test H₀: p₁ - p₂ ≤ .01,H_A: p₁ - p₂ > .01,at α = .05,where $\hat { p } _ { 1 }$ = .08, $\hat { p } _ { 2 }$ = .035,n₁ = 200,and n₂ = 400,what is the standard deviation used in the calculation of the test statistic?

Find a 98 percent confidence interval for the paired difference. $d_{1}-d_{2} \text { where } \overline{\mathrm{D}}=1.6, s_{d}^{2}=40.96, n=30$

When testing H₀: μ₁ - μ₂ = 2,H_A: μ₁ - μ₂ > 2,where $\bar { X } _ { 1 }$ = 522, $\bar { X } _ { 2 }$ = 516,σ₁² = 28,σ₂² = 24,n₁ = 40,n₂ = 30,at α = .01,what is the test statistic?