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

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

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

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.

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

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.

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

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.

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?

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

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.

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.

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

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?

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.

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?

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

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

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.

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.