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

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Question 1

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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.

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Question 2

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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.

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Question 3

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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.

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.

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?

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?

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?

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

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.

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.

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.

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.

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?

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

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

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.

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

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?

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:

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