Question 1

Find a 95 percent confidence interval for μ₁ − μ₂,where n₁ = 15,n₂ = 10, = 1.94, = 1.04,s₁² = .2025,and s₂² = .0676.(Assume equal population variances. )

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

In comparing the difference between two independent population means,the sampling distributions of the population means are at least approximately ________________.
A) skewed right
B) skewed left
C) normal
D) binomial

Accepted Answer

The central limit theorem states that as sample size increases, the sampling distribution of the sample mean approaches a normal distribution regardless of the shape of the population from which the sample is drawn. Therefore, the sampling distributions of the population means will be approximately normal in comparing the difference between two independent population means.

Question 4

In testing the difference between the means of two independent populations,the variances of the two samples can be pooled if the population variances are assumed to ____________.
A) be unequal
B) be greater than the mean
C) sum to 1
D) be equal

Accepted Answer

The variances of the two populations need to be assumed to be equal in order to pool the variances of the two samples. This assumption allows for a more precise estimate of the common population variance, which in turn improves the accuracy of the hypothesis test for the difference between the means.

Question 5

When comparing two independent population variances,the correct test statistic to use is __________. A) z B) t C) F D) t²

Accepted Answer

The F-test is used to compare two independent population variances.

Question 6

Find a 98 percent confidence interval for the paired difference

Accepted Answer

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

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 ____. A) z B) t C) F D) t²

Accepted Answer

When testing the difference for the population of paired differences, we are using dependent samples. In such cases, we use the t-test instead of the z-test. The t-test is used because the population standard deviation is unknown and must be estimated from the sample. The correct test statistic to use is therefore t.

Question 8

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

The purpose of matching pairs is to reduce the variation attributable to differences between individual observations, which can bias the results of a test of means. By reducing this variation, the test is able to more accurately determine if the means of the two related populations are different. Therefore, the correct answer is D) variation.

Question 9

Find a 95 percent confidence interval for μ₁ − μ₂,where n₁ = 50,n₂ = 75, = 82, = 76,s₁² = 8,and s₂² = 6.Assume unequal variances.

Accepted Answer

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

Question 10

When comparing the variances of two normally distributed populations using independent random samples,the correct test statistic to use is __________.
A) z
B) t
C) F
D) chi-square
E) None of the other choices is correct.

Accepted Answer

The correct test statistic to use is the F-test which compares the ratio of the variances of the two populations. The F-test is appropriate for comparing the variances of two normal populations with independent random samples. The z-test is used to compare means of two normal populations with known variances, the t-test is used to compare means of two normal populations with unknown variances and small sample sizes, and the chi-square test is used to test for independence or goodness of fit in categorical data.

Question 11

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

Accepted Answer

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

Question 12

Two independent samples selected from two normally distributed populations have variances of σ₁² and σ₂² with n₁ = 10 and n₂ = 15.The degrees of freedom for the F distribution when testing the equality of the two population variances are A) 10 and 15. B) 11 and 16. C) 9 and 14. D) 8 and 13.

Accepted Answer

The degrees of freedom for the F distribution when testing the equality of the two population variances are calculated as (n1-1) and (n2-1), where n1 and n2 are the sample sizes of the two populations. Therefore, for the given problem, the degrees of freedom are (10-1) and (15-1), which simplifies to 9 and 14. Hence, the correct choice is C.

Question 13

In testing the equality of population variance,what assumption(s)should be considered?
A) independent samples
B) equal sample sizes
C) normal distribution of the populations
D) independent samples and equal sample sizes
E) independent samples and normal distribution of the populations

Accepted Answer

The assumption of independent samples needs to be considered because this test involves comparing two separate samples. The assumption of normal distribution of the populations is also important because the test statistic, F, is based on the ratio of sample variances, which is only valid if the populations are normally distributed. Equal sample sizes is not a necessary assumption for testing the equality of population variance, but it can be helpful in increasing the power of the test.

Question 14

In order to test the effectiveness of a drug called XZR designed to reduce cholesterol levels,the cholesterol levels of 9 heart patients are measured before they are given the drug.The same 9 patients use XZR for two continuous months.After two months of continuous use,the cholesterol levels are measured again.The comparison of cholesterol levels before versus after the administration of the drug is an example of testing the difference between two ____________.
A) samples of equal variances
B) independent samples
C) paired samples
D) samples of unequal variances

Accepted Answer

The comparison of cholesterol levels before and after the administration of the drug involves the same 9 heart patients, meaning that the two samples are paired. Therefore, the best choice for testing the difference is paired samples. Choices A, B, and D are not appropriate because they do not reflect the paired nature of the samples.

Question 15

When we test H₀: p₁ − p₂ £ .01,H_A: p₁ − p₂ > .01,at α = .05,where ₁ = .08, ₂ = .035,n₁ = 200,and n₂ = 400,what is the standard deviation used to calculate the test statistic?

Accepted Answer

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

Question 16

Parameters of the F distribution include A) n₁. B) degrees of freedom for the numerator and the denominator. C) n₂. D) n₁ and n₂. E) None of the other choices is correct.

Accepted Answer

The F distribution is a ratio of two chi-square distributions divided by their respective degrees of freedom. Therefore, the parameters of the F distribution include the degrees of freedom for the numerator and the denominator.

Question 17

In general,the shape of the F distribution is _________.
A) skewed right
B) skewed left
C) normal
D) binomial

Accepted Answer

The F distribution is skewed right, as it has a longer right tail due to its dependence on the ratio of two independent chi-squared distributions.

Question 18

In testing the difference between two independent population means,if the assumption is of unequal variances,the critical value of the t statistic is obtained by calculating the ___________________. A) degrees of freedom B) sum of the two sample sizes (n₁ + n₂) C) p-value D) pooled variance

Accepted Answer

As the degrees of freedom increase, then the curve starts to approximate the normal distribution.

Question 19

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

The degrees of freedom for a paired t-test is calculated as df = n-1, where n is the number of pairs. In this case, n = 8, so df = 8-1 = 7. Therefore, the correct choice is B.

Question 20

In testing the difference between two independent population means,it is assumed that the level of measurement is at least ______________.
A) a ratio variable
B) a qualitative variable
C) an interval variable
D) a categorical variable

Accepted Answer

In order to test the difference between two independent population means, we need to calculate the t-statistic or z-score, which requires the level of measurement to be at least interval scale. This is because the difference between two means should be meaningful and consistent, and only interval or ratio variables provide this type of measurement. Qualitative and categorical variables do not have a consistent unit of measurement, making it impossible to calculate the difference between means. Therefore, choice C, an interval variable, is the best choice for this question.

Quiz 10: Statistical Inferences for Means and Proportions

Find a 95 percent confidence interval for μ₁ − μ₂,where n₁ = 15,n₂ = 10, = 1.94, = 1.04,s₁² = .2025,and s₂² = .0676.(Assume equal population variances. )

Using a 90 percent confidence interval of [−.0076,.0276] for the difference between the proportions of failures in factory 1 and factory 2,where ₁ = .05, 11ec8feb_23a3_8c8d_bdf7_a512f9d1bbd7_TB2569_11₂ = .04,n₁ = 500,and n₂ = 2000,can we reject the null hypothesis at α = .10?

In comparing the difference between two independent population means,the sampling distributions of the population means are at least approximately ________________.

In testing the difference between the means of two independent populations,the variances of the two samples can be pooled if the population variances are assumed to ____________.

When comparing two independent population variances,the correct test statistic to use is __________.

Find a 98 percent confidence interval for the paired difference

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 ____.

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.

Find a 95 percent confidence interval for μ₁ − μ₂,where n₁ = 50,n₂ = 75, = 82, = 76,s₁² = 8,and s₂² = 6.Assume unequal variances.

When comparing the variances of two normally distributed populations using independent random samples,the correct test statistic to use is __________.

Find a 90 percent confidence interval for the difference between the proportions of failures in factory 1 and factory 2,where ₁ = .05, 11ec8feb_055f_e61c_bdf7_7733cc20d01e_TB2569_11₂ = .04,n₁ = 500,and n₂ = 2000.

Two independent samples selected from two normally distributed populations have variances of σ₁² and σ₂² with n₁ = 10 and n₂ = 15.The degrees of freedom for the F distribution when testing the equality of the two population variances are

In testing the equality of population variance,what assumption(s) should be considered?

When we test H₀: p₁ − p₂ £ .01,H_A: p₁ − p₂ > .01,at α = .05,where ₁ = .08, 11ec8fe3_f0fe_0507_bdf7_b1edfdb0dc11_TB2569_11₂ = .035,n₁ = 200,and n₂ = 400,what is the standard deviation used to calculate the test statistic?

Parameters of the F distribution include

In general,the shape of the F distribution is _________.

In testing the difference between two independent population means,if the assumption is of unequal variances,the critical value of the t statistic is obtained by calculating the ___________________.

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 two independent population means,it is assumed that the level of measurement is at least ______________.

Quiz 10: Statistical Inferences for Means and Proportions

Find a 95 percent confidence interval for μ1 − μ2,where n1 = 15,n2 = 10, = 1.94, = 1.04,s12 = .2025,and s22 = .0676.(Assume equal population variances. )

Using a 90 percent confidence interval of [−.0076,.0276] for the difference between the proportions of failures in factory 1 and factory 2,where 1 = .05, 11ec8feb_23a3_8c8d_bdf7_a512f9d1bbd7_TB2569_112 = .04,n1 = 500,and n2 = 2000,can we reject the null hypothesis at α = .10?

In comparing the difference between two independent population means,the sampling distributions of the population means are at least approximately ________________.

In testing the difference between the means of two independent populations,the variances of the two samples can be pooled if the population variances are assumed to ____________.

When comparing two independent population variances,the correct test statistic to use is __________.

Find a 98 percent confidence interval for the paired difference

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 ____.

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.

Find a 95 percent confidence interval for μ1 − μ2,where n1 = 50,n2 = 75, = 82, = 76,s12 = 8,and s22 = 6.Assume unequal variances.

When comparing the variances of two normally distributed populations using independent random samples,the correct test statistic to use is __________.

Find a 90 percent confidence interval for the difference between the proportions of failures in factory 1 and factory 2,where 1 = .05, 11ec8feb_055f_e61c_bdf7_7733cc20d01e_TB2569_112 = .04,n1 = 500,and n2 = 2000.

Two independent samples selected from two normally distributed populations have variances of σ12 and σ22 with n1 = 10 and n2 = 15.The degrees of freedom for the F distribution when testing the equality of the two population variances are

In testing the equality of population variance,what assumption(s) should be considered?

When we test H0: p1 − p2 £ .01,HA: p1 − p2 > .01,at α = .05,where 1 = .08, 11ec8fe3_f0fe_0507_bdf7_b1edfdb0dc11_TB2569_112 = .035,n1 = 200,and n2 = 400,what is the standard deviation used to calculate the test statistic?

Parameters of the F distribution include

In general,the shape of the F distribution is _________.

In testing the difference between two independent population means,if the assumption is of unequal variances,the critical value of the t statistic is obtained by calculating the ___________________.

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 two independent population means,it is assumed that the level of measurement is at least ______________.

Find a 95 percent confidence interval for μ₁ − μ₂,where n₁ = 15,n₂ = 10, = 1.94, = 1.04,s₁² = .2025,and s₂² = .0676.(Assume equal population variances. )

Using a 90 percent confidence interval of [−.0076,.0276] for the difference between the proportions of failures in factory 1 and factory 2,where ₁ = .05, 11ec8feb_23a3_8c8d_bdf7_a512f9d1bbd7_TB2569_11₂ = .04,n₁ = 500,and n₂ = 2000,can we reject the null hypothesis at α = .10?

Find a 95 percent confidence interval for μ₁ − μ₂,where n₁ = 50,n₂ = 75, = 82, = 76,s₁² = 8,and s₂² = 6.Assume unequal variances.

Find a 90 percent confidence interval for the difference between the proportions of failures in factory 1 and factory 2,where ₁ = .05, 11ec8feb_055f_e61c_bdf7_7733cc20d01e_TB2569_11₂ = .04,n₁ = 500,and n₂ = 2000.

Two independent samples selected from two normally distributed populations have variances of σ₁² and σ₂² with n₁ = 10 and n₂ = 15.The degrees of freedom for the F distribution when testing the equality of the two population variances are

When we test H₀: p₁ − p₂ £ .01,H_A: p₁ − p₂ > .01,at α = .05,where ₁ = .08, 11ec8fe3_f0fe_0507_bdf7_b1edfdb0dc11_TB2569_11₂ = .035,n₁ = 200,and n₂ = 400,what is the standard deviation used to calculate the test statistic?

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 ____.