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 A) 22 B) 21 C) 19 D) 20

Exam 10: Comparing Two Means and Two Proportions

A market research study conducted by a local winery on white wine preference found the following results.Of a sample of 500 men,120 preferred white wine.Of a sample of 500 women,210 preferred white wine.What do you conclude at α = .05 about the claim that women's preference for white wine is 25 percent higher than men's?

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Question 1

Correct Answer:

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Cannot reject the null hypothesis.In this study,women's preference for white wine was not 25 percent higher than men's.
Feedback: $\hat{p}_{w}=.42, \hat{p}_{m}=.24$

$z=\frac{\left(\hat{p}_{w}-\hat{p}_{m}\right)-.25}{\sqrt{\frac{\hat{p}_{w}\left(1-\hat{p}_{w}\right)}{n_{w}}+\frac{\hat{p}_{m}\left(1-\hat{p}_{m}\right)}{n_{m}}}}=\frac{.18-.25}{\sqrt{.0004872+.0003648}}=\frac{-.07}{\sqrt{.000852}}=-2.397$
Critical value z = 1.645
-2.397 is not greater than 1.645,so do not reject the null hypothesis.

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. )

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Question 2

Correct Answer:

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(0.573 1.227)
Feedback: $s^{2}=\frac{(15-1)(.45)^{2}+(10-1)(.26)^{2}}{15+10-2}=.1497$

$s_{\bar{X}_{1}-\bar{x}_{2}}=\sqrt{.1497\left(\frac{1}{15}+\frac{1}{10}\right)}=.158$

$(1.94-1.04) \pm(2.069)(.158) \rightarrow .573 \text { to } 1.227$

Calculate the t statistic for testing equality of means where

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Question 3

Correct Answer:

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$\bar { X } _ { 1 }$
= 8.2, $\bar { X } _ { 2 }$
= 11.3,s₁² = 5.4,s₂² = 5.2,n₁ = 6,and n₂ = 7.(Assume equal population variances. )
-2.42
Feedback:s² = ((6 - 1)(5.4)+ (7 - 1)(5.2))/(6 + 7 - 2)= 5.291
s = √[5.291(1/6 + 1/7)] = 1.2797
t = (8.2 - 11.3)/1.2797 = -2.42

A test of spelling ability is given to a random sample of 10 students before and after they complete a spelling course.The mean score before the course was 119.60,and after the course the mean score was 130.80.The standard deviation of the difference is 16.061.Calculate a 99 percent confidence interval.

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Question 4

The registrar at a state college is interested in determining whether there is a difference of more than one credit hour between male and female students in the average number of credit hours taken during a term.She selected a random sample of 60 male and 60 female students and observed the following sample information. Male Female Sample Mean 13.24 14.68 Population Std Dev 1.2 1.56 Sample Size 60 60 Calculate the test statistic to be used in the analysis.Assume unequal variances.

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Question 5

Suppose that a realtor is interested in comparing the price of midrange homes in two cities in a midwestern state.She conducts a small survey in the two cities,looking at the price of midrange homes.Assume equal population variances. City A City B Sample Mean 86,900 84,000 Sample Std Dev 2300 1750 Sample Size 9 7 Test the claim at α = .01.

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Question 6

Two hospital emergency rooms use different procedures for triage of their patients.We want to test the claim that the mean waiting time of patients is the same for both hospitals.The 40 randomly selected subjects from one hospital produce a mean of 18.3 minutes.The 50 randomly selected patients from the other hospital produce a mean of 25.31 minutes.Sample standard deviations are s_a = 2.1 minutes and s_b = 2.92 minutes.Set up the null hypothesis to determine whether there is a difference in the mean waiting time between the two hospitals.

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Question 7

When testing the difference for the population of paired differences in which two different observations are taken on the same units,the correct test statistic to use is ____.

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Question 8

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?

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Question 9

Let p₁ represent the population proportion of U.S.senatorial and congressional (House of Representatives)Democrats who are in favor of a new modest tax on "junk food." Let p₂ represent the population proportion of U.S.senatorial and congressional Republicans who are in favor of a new modest tax on "junk food." Out of the 265 Democratic senators and members of Congress,106 of them are in favor of a "junk food" tax.Out of the 285 Republican senators and members of Congress,only 57 are in favor of a "junk food" tax.Find a 95 percent confidence interval for the difference between proportions l and 2.

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Question 10

A market research study conducted by a local winery on white wine preference found the following results.Of a sample of 500 men,120 preferred white wine.Of a sample of 500 women,210 preferred white wine.Calculate the test statistic for testing the claim that the percentage of women preferring white wine is 25 percent higher than that of men.

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Question 11

In testing the difference between two means from two normally distributed independent populations,the distribution of the difference in sample means will be:

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Question 12

At α = .10,testing the hypothesis that the proportion of consumer industry companies' (CON)winter-quarter profit growth is more than 2 percent greater than the proportion of banking companies' (BKG)winter-quarter profit growth,given that $\hat { p }_{ CON } = .20 ,$ $\hat { p } _ { B K G } = .14 ,$ n_CON = 300,and n_BKG = 400,calculate the estimated standard deviation for the model.

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Question 13

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.

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Question 14

A coffee shop franchise owner is looking at two possible locations for a new shop.To help him decide,he looks at the number of pedestrians that go by each of the two locations in one-hour segments.At location A,counts are taken for 35 one-hour units,with a mean number of pedestrians of 421 and a sample standard deviation of 122.At the second location (B),counts are taken for 50 one-hour units,with a mean number of pedestrians of 347 and a sample standard deviation of 85.Assume the two population variances are not known but are equal.Calculate a 95 percent confidence interval for the difference in pedestrian traffic at the two locations.

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Question 15

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 ___________.

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Question 16

If the limits of the confidence interval of the difference between the means of two normally distributed populations were 8.5 and 11.5 at the 95 percent confidence level,then we can conclude that we are 95 percent certain that there is a significant difference between the two population means.

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Question 17

Two hospital emergency rooms use different procedures for triage of their patients.We want to test the claim that the mean waiting time of patients is the same for both hospitals.The 40 randomly selected subjects from one hospital produce a mean of 18.3 minutes.The 50 randomly selected patients from the other hospital produce a mean of 25.31 minutes.Assume s_a = 2.1 minutes and s_b = 2.92 minutes.Calculate the test statistic for testing the hypothesis that there is a difference in the mean waiting time between the two hospitals.Assume unequal variances.

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Question 18

In testing the difference between the means of two normally distributed populations using independent random samples,the alternative hypothesis always indicates no differences between the two specified means.

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Question 19

Suppose that a realtor is interested in comparing the price of midrange homes in two cities in a midwestern state.She conducts a small survey in the two cities,looking at the price of midrange homes.Assume equal population variances. City A City B Sample Mean 86,900 84,000 Sample Std Dev 2300 1750 Sample Size 9 7 Set up the alternative hypothesis to test the claim that there is a difference in the mean price of midrange homes of the two cities.

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Question 20

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. )

Calculate the t statistic for testing equality of means where

When testing the difference for the population of paired differences in which two different observations are taken on the same units,the correct test statistic to use is ____.

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?

In testing the difference between two means from two normally distributed independent populations,the distribution of the difference in sample means will be:

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.

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 ___________.

If the limits of the confidence interval of the difference between the means of two normally distributed populations were 8.5 and 11.5 at the 95 percent confidence level,then we can conclude that we are 95 percent certain that there is a significant difference between the two population means.

In testing the difference between the means of two normally distributed populations using independent random samples,the alternative hypothesis always indicates no differences between the two specified means.

An Introduction to Business Statistics

Descriptive Statistics: Tabular and Graphical Methods

Descriptive Statistics: Numerical Methods

Probability

Discrete Random Variables

Continuous Random Variables

Sampling and Sampling Distributions

Confidence Intervals

Hypothesis Testing

Filters

Exam 10: Comparing Two Means and Two Proportions

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. )

Calculate the t statistic for testing equality of means where

When testing the difference for the population of paired differences in which two different observations are taken on the same units,the correct test statistic to use is ____.

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?

In testing the difference between two means from two normally distributed independent populations,the distribution of the difference in sample means will be:

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.

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 ___________.

If the limits of the confidence interval of the difference between the means of two normally distributed populations were 8.5 and 11.5 at the 95 percent confidence level,then we can conclude that we are 95 percent certain that there is a significant difference between the two population means.

In testing the difference between the means of two normally distributed populations using independent random samples,the alternative hypothesis always indicates no differences between the two specified means.

An Introduction to Business Statistics

Descriptive Statistics: Tabular and Graphical Methods

Descriptive Statistics: Numerical Methods

Probability

Discrete Random Variables

Continuous Random Variables

Sampling and Sampling Distributions

Confidence Intervals

Hypothesis Testing

Filters

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. )

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?

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.

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 ___________.