Deck 10: Hypothesis Tests for Proportions, Mean Differences and Proportion Differences

Question 1

One of the differences between conducting a two-tailed hypothesis test for the difference between two population means versus a one-tailed test is that the value of the test statistic becomes larger.

Answer 1

False

Question 2

The level of significance in a hypothesis test for a population proportion is the probability of accepting a false null hypothesis.

Answer 2

False

Question 3

You are using independent samples of size 10 to test whether two population means are equal, with $\mu$ ₁ = $\mu$ ₂ as the null hypothesis.If the populations are normal and have equal standard deviations, it would be appropriate to use a pooled sample standard deviation in your test.

Answer 3

True

Question 4

You are using independent samples of size 150 to test whether two population proportions are equal, with $\pi$ ₁ = $\pi$ ₂ as the null hypothesis.If the sample proportion difference is statistically significant at the 5% significance level, it will also be statistically significant at the 10% significance level.

Question 5

You are using a sample of size 225 to conduct a hypothesis test in which you want to determine whether a certain population proportion $\pi$ has changed since last year.If the null hypothesis is $\pi$ = .25 and the p-value for the this two-tailed test turns out to be .0263, you should conclude, at the .05 significance level, that the population proportion has, in fact, changed.

Question 6

You are using independent samples of size 100 to test whether two population proportions are equal, with $\pi$ ₁ = $\pi$ ₂ as the null hypothesis.In this test, it would be appropriate to use the pooled sample proportion in an estimate of the standard error for your test.

Question 7

The sampling distribution of the sample proportion is the probability distribution of all possible values of the sample proportion when a sample size n is taken from a particular population.

Question 8

You are using independent samples of size 12 each to test whether two population means are equal, with $\mu$ ₁ = $\mu$ ₂ as the null hypothesis.If the p-value for the test turns out to be .0113, you should conclude, at the .01 significance level, that the population means are not the equal.

Question 9

You are using independent samples to test whether two population means are equal, with $\mu$ ₁ = $\mu$ ₂ as the null hypothesis.If the p-value for the test leads you to reject the null hypothesis at the 5% significance level, it will also lead you to reject the null hypothesis at the 1% significance level.

Question 10

A matched sample design often leads to a smaller sampling error than the independent sample design because variation between sampled items is reduced or eliminated as a source of sampling error.

Question 11

You are using a sample of size 100 to conduct a hypothesis test in which you want to determine whether a certain population proportion $\pi$ has increased since last year.If the null hypothesis is $\pi$ < .33 and the test statistic turns out to be 2.13, you should conclude, at the .05 significance level, that the population proportion has, in fact, increased.

Question 12

You are using a sample of size 120 to conduct a hypothesis test in which you want to determine whether a certain population proportion $\pi$ has changed since last year.If the null hypothesis is $\pi$ = .25 and the test statistic turns out to be 1.83, you should conclude, at the .05 significance level, that the population proportion has, in fact, changed.

Question 13

In a matched sample design, one uses the average for each pair of data values when building a confidence interval.

Question 14

The sampling distribution of the difference between two sample proportions is approximately normal whenever n $\ge$ 30.

Question 15

In hypothesis test for the difference between two population means, the critical value is a number that establishes the boundary of the reject H₀ region.

Question 16

The positive critical value for a two-tailed hypothesis test of the difference between two population means is larger than for a one-tailed hypothesis test given the same level of significance.

Question 17

You are using a sample of size 200 to conduct a hypothesis test in which you want to determine whether a certain population proportion $\pi$ has decreased since last year.If the null hypothesis is $\pi$ > .5 and the test statistic turns out to be -1.74, you should conclude, at the .05 significance level, that the population proportion has, in fact, decreased.

Question 18

You are using independent samples of size 14 to test whether two population means are equal, with $\mu$ ₁ = $\mu$ ₂ as the null hypothesis.If the populations are normal and have unequal variances, it would be appropriate to use a pooled sample standard deviation in your test.

Question 19

You are using a sample of size 150 to conduct a hypothesis test in which you want to determine whether a certain population proportion $\pi$ has decreased since last year.If the null hypothesis is $\pi$ > .5 and the p-value for the test turns out to be .0324, you should conclude, at the .05 significance level, that the population proportion has, in fact, decreased.

Question 20

For a hypothesis test involving the difference between two proportions, the pooled sample proportion is a weighted average of the two individual sample proportions.

Question 21

For a hypothesis test in which the null hypothesis is $\pi$ ₁ - $\pi$ ₂ = $\pi$ , which of the following statements must be true?

A)To reject the null hypothesis, $\pi$ ₁ cannot be less than $\pi$ ₂.
B)Failing to reject the null hypothesis will mean that $\pi$ ₁ and $\pi$ ₂ are equal.
C)The sample proportions can only be approximated.
D)The null hypothesis can only be rejected if the sample proportions are not equal.

Question 22

If we are interested in making the case that the proportion in Population 1 is larger than the proportion in Population 2, and we plan to use the contrary position as the null hypothesis, then the

A)null hypothesis should state $\pi$ ₁- $\pi$ ₂ < 0.
B)null hypothesis should state $\pi$ ₁- $\pi$ ₂ > 0.
C)alternative hypothesis should state $\pi$ ₁- $\pi$ ₂ $\ge$ 0.
D)alternative hypothesis should state $\pi$ ₁- $\pi$ ₂ < 0.
E)none of the above.

Question 23

For a hypothesis test in which the null hypothesis is $\mu$ ₁ - $\mu$ ₂ > 0, which of the following statements must be true?

A)To reject the null hypothesis, $\mu$ ₁ cannot be less than $\mu$ ₂.
B)Failing to reject the null hypothesis will mean that $\mu$ ₁ and $\mu$ ₂ are equal.
C)The sample means will be different.
D)The null hypothesis can only be rejected if the sample means are not equal.

Question 24

Independent samples are obtained from two normal populations with unknown but equal standard deviations (variances) in order to construct a hypothesis test for the difference between the population means.If the first sample contains 20 items and the second sample contains 25 items, the correct form to use for the sampling distribution is the

A)normal distribution
B)t distribution with 43 degrees of freedom
C)t distribution with 45 degrees of freedom
D)F distribution with 20 and 25 degrees of freedom
E)none of the above

Question 25

If we are interested in testing a null hypothesis that the mean of Population 1 is smaller than the mean of Population 2, the

A)null hypothesis should state $\mu$ ₁ - $\mu$ ₂ < 0
B)null hypothesis should state $\mu$ ₁ - $\mu$ ₂ > 0
C)alternative hypothesis should state $\mu$ ₁ - $\mu$ ₂ $\ge$ 0
D)alternative hypothesis should state $\mu$ ₁ - $\mu$ ₂ < 0
E)none of the above

Question 26

You are testing the difference between two population means.The pooled standard deviation is only appropriate if the two populations

A)are normally distributed
B)have equal variances (standard deviations)
C)have equal means (averages)
D)are skewed
E)have equal sample sizes

Question 27

Independent samples are obtained from two normal populations with unknown but equal variances in order to construct a hypothesis test for the difference between the population means.If the first sample contains 16 items and the second sample contains 26 items, the correct form to use for the sampling distribution is the

A)normal distribution
B)t distribution with 15 degrees of freedom
C)t distribution with 25 degrees of freedom
D)t distribution with 40 degrees of freedom
E)none of the above

Question 28

In large sample cases, using a significance level of 5% in a one-tailed test in which the null hypothesis is $\pi$ ₁ < $\pi$ ₂, the decision rule is:

A)Reject the null hypothesis if $\pi$ ₁ - $\pi$ ₂ is greater than 0.
B)Reject the null hypothesis if the test statistic, z_stat, is either greater than −1.65 or less than +1.65.
C)Reject the null hypothesis if the p-value for the sample mean difference is less than .05.
D)Reject the null hypothesis if the difference in sample proportions is greater than 0.

Question 29

In a one-tailed hypothesis test in which the null hypothesis is $\mu$ ₁ > $\mu$ ₂, sample sizes were 12 for sample 1 and 16 for sample 2.Which of the following statements is true?

A)If the two populations are normal, with equal standard deviations, we can pool sample standard deviations to estimate the common population standard deviation.
B)We could use the t distribution with df = 28 to conduct the test.
C)The sample mean difference can only be approximated.
D)The p-value for the sample mean difference would necessarily be less than $\alpha$ .

Question 30

In a one-tailed hypothesis test in which the null hypothesis is $\pi$ ₁ < $\pi$ ₂, suppose sample results lead you to reject the null hypothesis at the 1% significance level.Which of the following statements would be accurate?

A) $\pi$ ₁ - $\pi$ ₂ must be greater than 0.
B)the test statistic, z_stat, is between −2.33 and +2.33.
C)the test statistic, z_stat, is less −2.33.
D)the p-value for the sample proportion difference is less than .01.

Question 31

For large sample cases, in a two-tailed test of the difference between two population means (significance level = 5%), the decision rule is:

A)Reject the null hypothesis if the test statistic, z_stat, is either less than −1.96 or greater than +1.96.
B)Reject the null hypothesis if the test statistic, z_stat, is either greater than −1.96 or less than +1.96.
C)Reject the null hypothesis if the p-value is greater than .05.
D)Reject the null hypothesis if the test statistic, t_stat, is either less than −1.022 or greater than +1.022.

Question 32

In a one-tailed hypothesis test in which the null hypothesis is $\mu$ ₁ > $\mu$ ₂, suppose sample results lead you to reject the null hypothesis at the 1% significance level.Which of the following statements must be true?

A) $\mu$ ₁ - $\mu$ ₂ must be greater than 0.
B)you would also reject the null hypothesis at the 5% significance level.
C)the sample mean difference is not statistically significant at the 5% significance level.
D)the p-value for the sample mean difference could be.025.

Question 33

Assume we are interested in determining whether the proportion of voters planning to vote for candidate A (define this proportion as $\pi$ _A) is less than the proportion of voters planning to vote for candidate B (define this proportion as $\pi$ _B) using the contrary position as the null hypothesis.The correct set of hypotheses for testing here is

A)H₀: $\pi$ _A - $\pi$ _B < 0; H_a: $\pi$ _A - $\pi$ _B $\ge$ 0
B)H₀: $\pi$ _A - $\pi$ _B $\ge$ 0; H_a: $\pi$ _A - $\pi$ _B < 0
C)H₀: $\pi$ _A - $\pi$ _B = 0; H_a: $\pi$ _A - $\pi$ _B $\neq$ 0
D)H₀: $\pi$ _A - $\pi$ _B $\le$ 0; H_a: $\pi$ _A - $\pi$ _B > 0
E)none of the above

Question 34

In a hypothesis test in which the null hypothesis states that the difference between two population proportions is 0, that is, when $\pi$ ₁ = $\pi$ ₂, which of the following occurs?

A)a common pooled value is calculated as a weighted average of the individual sample proportions
B)a one-tailed hypothesis test is performed
C) the t distribution is used
D)the sampling distribution is positively skewed
E)all of the above

Question 35

You are testing the difference between two population means.Which of the following best describes the pooled sample standard deviation under the assumption that the two population standard deviations are equal for small samples?

A)it is the square root of the weighted average of the sample variances, weighted by their respective degrees of freedom
B)it is a simple average of the sample standard deviations
C)it cannot be calculated for small samples
D)it is the square of the differences of the sample variances
E)none of the above

Question 36

Which of the following statements about the sampling distribution of the sample proportion is TRUE?

A)it is approximately normal, so long as n $\pi$ > 5 and n(1 - $\pi$ ) > 5
B)it is centered on the population proportion $\pi$
C)it has standard deviation equal to the square root of $\pi$ (1- $\pi$ )/n.
D)b and c only
E)all of the above

Question 37

For a one-tailed hypothesis test in which the null hypothesis is $\pi$ > 7and sample size is 150, which of the following statements is true?

A)Pooling sample standard deviations would be appropriate.
B)We could use the normal distribution to conduct the test.
C)The sample proportion can only be approximated.
D) $\pi$ cannot be less than .7.

Question 38

In a two-tailed hypothesis test in which the null hypothesis is $\mu$ ₁ = $\mu$ ₂, suppose sample results lead you to reject the null hypothesis at the 5% significance level.Which of the following statements must be true?

A) $\mu$ ₁ - $\mu$ ₂ must be greater than 0.
B)you would also reject the null hypothesis at the 1% significance level.
C)the sample mean difference is statistically significant at the 5% level and above.
D)the p-value for the sample mean difference could be.075.

Question 39

You are testing the difference between two population means.The sample sizes are small.Under the assumption that the standard deviations of the two populations are equal and using a pooled estimator for the standard deviation, which of the following statements is true?

A)the sample size must be increased in order to conduct a proper test
B)the standard normal distribution can be used
C)the t distribution with n₁ + n₂ degrees of freedom is used
D)the t distribution with n₁ + n₂ - 2 degrees of freedom is used
E)none of the above