At $\alpha=.05$, what is your conclusion?

The Employment and Training Administration reported that the U.S. mean unemployment insurance benefit was $238 per week (The World Almanac, 2003). A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was below the national average.

At$\alpha$ = .05, what is your conclusion?

The Employment and Training Administration reported that the U.S. mean unemployment insurance benefit was $238 per week (The World Almanac, 2003). A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was below the national average.

Develop appropriate hypotheses such that rejection of H0 will support the researcher’s contention.

During the 2003 Super Bowl, Miller Lite Beer’s commercial referred to as “The Miller Lite Girls” ranked among the top three most effective advertisements aired during the Super Bowl (USA Today, December 29, 2003). The survey of advertising effectiveness, conducted by USA Today’s Ad Track poll, reported separate samples by respondent age group to learn about how the Super Bowl advertisement appealed to different age groups. The following sample data apply to the “The Miller Lite Girls” commercial.

$$\begin{array}{ccc} {\textbf { Age Group}} & {\textbf {Sample Size}} & \begin{array}{c}{\textbf {Liked the }} \\ \textbf{Ad a Lot}\end{array}\\ \hline \text { Under 30} & 100& 49\\ \text {30 to 49} & 150&54 \end{array}$$

Conduct the hypothesis test and report the $p$-value. At α  .05, what is your conclusion?

Individuals filing federal income tax returns prior to March 31 received an average refund of $1056. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period.

b. For a sample of 400 individuals who filed a tax return between April 10 and 15 , the sample mean refund was$\$910$. Based on prior experience, a population standard deviation of $\sigma=\$ 1600$ may be assumed. What is the $p$-value?

Individuals filing federal income tax returns prior to March 31 received an average refund of $\$1056$. Consider the population of “last-minute” filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15).

a. A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of $\ H_0$ will support the researcher’s contention.

b. For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $\$910$. Based on prior experience a population standard deviation of $\sigma$ =$\$1600$ may be assumed. What is the p-value?

c. At $\alpha$ = .05, what is your conclusion?

d. Repeat the preceding hypothesis test using the critical value approach.

Individuals filing federal income tax returns prior to March 31 received an average refund of $1056. Consider the population of “last-minute” filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15).

A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of H0 will support the researcher’s contention.

The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is 14 automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan increases sales volume. To collect data on the plan, a sample of sales personnel will be allowed to sell under the new bonus plan for a one-month period.

Comment on the conclusion when $H _ { 0 }$ cannot be rejected.

The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is 14 automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan increases sales volume. To collect data on the plan, a sample of sales personnel will be allowed to sell under the new bonus plan for a one-month period.

Develop the null and alternative hypotheses most appropriate for this situation.

For the United States, the mean monthly Internet bill is $\$32.79$ per household (CNBC, January 18, 2006). A sample of 50 households in a southern state showed a sample mean of $\$30.63$. Use a population standard deviation of $\sigma$ = $\$5.60$.

a. Formulate hypotheses for a test to determine whether the sample data support the conclusion that the mean monthly Internet bill in the southern state is less than the national mean of $\$32.79$.

b. What is the value of the test statistic?

c. What is the p-value?

d. At $\alpha$= .01, what is your conclusion?

For the United States, the mean monthly Internet bill is $32.79 per household (CNBC, January 18, 2006). A sample of 50 households in a southern state showed a sample mean of$30.63. Use a population standard deviation of $\sigma$= $5.60.

At$\alpha$= .01, what is your conclusion?

For the United States, the mean monthly Internet bill is $32.79 per household (CNBC, January 18, 2006). A sample of 50 households in a southern state showed a sample mean of$30.63. Use a population standard deviation of $\sigma$= $5.60.

What is the value of the test statistic?

For the United States, the mean monthly Internet bill is $32.79 per household (CNBC, January 18, 2006). A sample of 50 households in a southern state showed a sample mean of$30.63. Use a population standard deviation of $\sigma$= $5.60.

What is the p-value?

$BusinessWeek$ conducted a survey of graduates from $30$ top MBA programs ($BusinessWeek,$ September $22, ~2003$). On the basis of the survey, assume that the mean annual salary for male and female graduates $10$ years after graduation is $\$168,000$ and $\$117,000$, respectively. Assume the standard deviation for the male graduates is $\$40,000$, and for the female graduates it is $\$25,000.$

What is the probability that a simple random sample of $40$ male graduates will provide a sample mean within $\$10,000$ of the population mean, $\$168,000$?