Select the best answer. An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are (a)

$$H_0: \hat{p} = 0.5; H_a: \hat{p} > 0.5$$

(b)

$$H_0: p = 0.5; H_a: p > 0.5$$

(c)

$$H_0: p = 0.5; H_a: p < 0.5$$

(d)

$$H_0: p = 0.5; H_a: p \neq 0.5$$

(e)

$$H_0: p > 0.5; H_a: p = 0.5$$

Give an example of a feeling or a behavior that would be considered normal in one circumstance but might be considered a sign of a psychological disorder in another circumstance.

A 95% confidence interval for the proportion of viewers of a certain reality television show who are ơver 30 years old is (0.26, 0.35). Suppose the show's producers want to test the hypothesis $H_{0}: p=0.25$ against $H_{a}: p \neq 0.25.$ Which of the following is an appropriate conclusion for them to draw al the $\alpha=0.05$ significance level? (a) Fail to reject $H_{0};$ there is convincing evidence that the true.proportion of viewers of this reality TV show who are over 30 years old equals 0.25. (b) Fail to reject $H_{0};$ there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from 0.25. (c) Reject $H_{0};$ there is not convincing evidence that the true proportion of viewers of this reality TV show who ạre over 30 years old differs from 0.25. (d) Reject $H_{0};$ there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old is greater than 0.25. (e) Reject $H_{0};$ there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from 0.25.

An opinion poll based on a small sample can be unrepresentative of the population. To see why, assume that 40% of the electorate favors a certain candidate. If a random sample of 7 is asked their preference, what is the probability that a majority will favor this candidate?

Select the best answer. At a baseball game, 42 of 65 randomly selected people own an iPod. At a rock concert occurring at the same time across town, 34 of 52 randomly selected people own an iPod. A researcher wants to test the claim that the proportion of iPod owners at the two venues is different. A 90% confidence interval for the difference in population proportions (game - concert) is (-0.154, 0.138). Which of the following gives the correct outcome of the researcher's test of the claim? (a) Because the confidence interval includes 0, the researcher can conclude that the proportion of iPod owners at the two venues is the same. (b) Because the center of the interval is -0.008, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game. (c) Because the confidence interval includes 0, the researcher cannot conclude that the proportion of iPod owners at the two venues is different. (d) Because the confidence interval includes more negative than positive values, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game. (e) The researcher cannot draw a conclusion about a claim without performing a significance test.

A researcher plans to conduct a significance test at the $\alpha=0.01$ significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type II error for the particular alternative value of the parameter at which she computed the power is (a) 0.01. (b) 0.10. (c) 0.89. (d) 0.90. (e) 0.99.

Vigorous exercise helps people live several years longer (on the average ). Whether mild activities like slow walking extend life is not clear. Suppose that the added life expectancy from regular slow walking is just 2 months. A statistical test is more likely to find a significant increase in mean life if

(a) it is based on a very large random sample.

(b) it is based on a very small random sample.

(c) The size of the sample doesn't have any effect on the significance of the test.

Research several facilities in your community that are designed to help people who have disabilities. Create a poster detailing the different ways one of these facilities helps these people.

Use the rock cycle to explain how each rock type forms.

An opinion poll asks a sample of 500 adults whether they favor giving parents of school-age children vouchers that can be exchanged for education at any public or private school of their choice. Each school would be paid by the government on the basis of how many vouchers it collected. Suppose that in fact 45% of the population favor this idea. What is the probability that more than half of the sample are in favor? (Assume that the sample is an SRS.)

You use technology to carry out a significance test and get a P-value of 0.031. The correct conclusion is (a) accept $H_{a}$ at the $\alpha=0.05$ significance level. (b) reject $H_{0}$ at the $\alpha=0.05$ significance level. (c) reject $H_{0}$ at the $\alpha=0.01$ significance level. (d) fail to reject $H_{0}$ at the $\alpha=0.05$ significance level. (e) fail to reject $H_{a}$ at the $\alpha=0.05$ significance level.

The numbers of incorrect answers on a true-false competency test for a random sample of 15 students were recorded as follows: 2, 1, 3, 0, 1, 3, 6, 0, 3, 3, 5, 2, 1, 4, and 2. Calculate the variance using the formula

$$(a) S^2 = \frac{1}{n-1} \sum_{i=1}^{n} (X_i-\overline{X} )^2.$$

$$(b) S^2 = \frac{1}{n(n-1)} \biggr[ n \sum_{i=1}^n X_i^2 - \biggr( \sum_{i=1}^n X_i \biggr) ^2 \biggr].$$

To test $H_{0}: \mu=80$ versus $H_{1}: \mu<80$, a simple random sample of size n=22 is obtained from a population that is known to be normally distributed.

If $\bar{x}=76.9$ and s=8.5, compute the test statistic.

Tell whether each statement is true for all real numbers. If you think it is not, give a numerical example to support your answer. If a<b and c<d, then a-c<b-d.