Question 1

In estimating the difference between two population means, the estimate for the standard deviation of the sampling distribution of  is found by taking the square root of the sum of the two sample variances.

Accepted Answer

A) True 
 B)False

Question 2

If you wish to construct a confidence interval estimate for the difference between two population means, what would an increase in the sample sizes used result in?

Accepted Answer

A)  a decrease in the critical value z 
B)  a narrower confidence interval 
C)  a wider confidence interval 
D)  a confidence interval that contains 0

Question 3

When testing  vs.  , the observed value of the z-score was found to be -2.15. What is the p-value for this test?

Accepted Answer

A)  0.0158 
B)  0.0316 
C)  0.9684 
D)  0.9842

Question 4

What is the rejection region for testing  at the 0.05 level of significance?

Accepted Answer

A)  |z|  1.96 
C)  z > 1.645 
D)  z < 2.33

Question 5

A two-tailed test of hypothesis for a population mean  with a significance level  equal to 0.05 will have a critical value z equal to 0.475.

Accepted Answer

A) True 
 B)False

Question 6

Which of the following would be an appropriate null hypothesis to test a proportion?

Accepted Answer

A)  The sample proportion is equal to 0.60. 
B)  The population proportion is greater than 0.60. 
C)  The population proportion is equal to 0.60. 
D)  The population proportion is not equal to 0.60.

Question 7

If the power of a statistical test is 0.9207, then the probability of accepting a false null hypothesis is 0.0793.

Accepted Answer

A) True 
 B)False

Question 8

A one-tailed hypothesis test of the population proportion is used when the alternative hypothesis takes the form

Accepted Answer

A) True 
 B)False

Question 9

Which of the following conditions must hold before one can make use of the standard normal distribution for constructing a confidence interval estimate for the population proportion p?

Accepted Answer

A)  and) are both greater than 5, wheredenotes the sample proportion 
B)  np and n(1 - p) are both greater than 5 
C)  n(p +) and n(p -) are both greater than 5, wheredenotes the sample proportion 
D)  the sample size is greater than 5

Question 10

The z-test can be used to determine whether two population means are equal.

Accepted Answer

A) True 
 B)False

Question 11

The necessary conditions having been met, a two-tailed test is being conducted to test the difference between two population proportions. The two sample proportions are  and  , and the standard error of the sampling distribution of   is 0.0085. Under these circumstances, the calculated value of the test statistic will be z = 3.41.

Accepted Answer

A) True 
 B)False

Question 12

The sampling distribution of  is normal if the sampled populations are normal, and approximately normal if the populations are non-normal and the sample sizes  and  are large.

Accepted Answer

A) True 
 B)False

Question 13

The probabilities of committing Type I and Type II errors are related such that when one is increased, the other will increase as well.

Accepted Answer

A) True 
 B)False

Question 14

If you wish to test whether two populations means are the same, the appropriate null and alternative hypotheses would be  vs.

Accepted Answer

A) True 
 B)False

Question 15

The p-value or observed significance level measures the strength of the evidence against the alternative hypothesis.

Accepted Answer

A) True 
 B)False

Question 16

The sampling distribution of  is approximately normal, provided that the sample size is large enough (n > 30).

Accepted Answer

A) True 
 B)False

Question 17

Suppose in testing a hypothesis about a proportion, the z test statistic is computed to be 1.92. The null hypothesis should be rejected if the chosen level of significance is 0.01 and a two-tailed test is used.

Accepted Answer

A) True 
 B)False

Question 18

When formulating a hypothesis test about a population mean, the alternative hypothesis should avoid using an equality.

Accepted Answer

A) True 
 B)False

Question 19

The necessary conditions having been met, a lower-tailed test is being conducted for the difference between two population proportions. If the value of the test statistic is -2.43, then the null hypothesis cannot be rejected at  = 0.025.

Accepted Answer

A) True 
 B)False

Question 20

Suppose in testing a hypothesis about a proportion, the p-value is computed to be 0.038. The null hypothesis should be rejected if the chosen level of significance is 0.05.

Accepted Answer

A) True 
 B)False

Exam 9: A: large-Sample Tests of Hypotheses

In estimating the difference between two population means, the estimate for the standard deviation of the sampling distribution of is found by taking the square root of the sum of the two sample variances.

If you wish to construct a confidence interval estimate for the difference between two population means, what would an increase in the sample sizes used result in?

When testing vs. , the observed value of the z-score was found to be -2.15. What is the p-value for this test?

What is the rejection region for testing at the 0.05 level of significance?

A two-tailed test of hypothesis for a population mean with a significance level equal to 0.05 will have a critical value z equal to 0.475.

Which of the following would be an appropriate null hypothesis to test a proportion?

If the power of a statistical test is 0.9207, then the probability of accepting a false null hypothesis is 0.0793.

A one-tailed hypothesis test of the population proportion is used when the alternative hypothesis takes the form

Which of the following conditions must hold before one can make use of the standard normal distribution for constructing a confidence interval estimate for the population proportion p?

The z-test can be used to determine whether two population means are equal.

The sampling distribution of is normal if the sampled populations are normal, and approximately normal if the populations are non-normal and the sample sizes and are large.

The probabilities of committing Type I and Type II errors are related such that when one is increased, the other will increase as well.

If you wish to test whether two populations means are the same, the appropriate null and alternative hypotheses would be vs.

The p-value or observed significance level measures the strength of the evidence against the alternative hypothesis.

The sampling distribution of is approximately normal, provided that the sample size is large enough (n > 30).

Suppose in testing a hypothesis about a proportion, the z test statistic is computed to be 1.92. The null hypothesis should be rejected if the chosen level of significance is 0.01 and a two-tailed test is used.

When formulating a hypothesis test about a population mean, the alternative hypothesis should avoid using an equality.

The necessary conditions having been met, a lower-tailed test is being conducted for the difference between two population proportions. If the value of the test statistic is -2.43, then the null hypothesis cannot be rejected at = 0.025.

Suppose in testing a hypothesis about a proportion, the p-value is computed to be 0.038. The null hypothesis should be rejected if the chosen level of significance is 0.05.