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.

a. Develop appropriate hypotheses such that rejection of $\ H_0$ will support the researcher’s contention.

b. For a sample of 100 individuals, the sample mean weekly unemployment insurance benefit was $\$231$ with a sample standard deviation of $80. What is the p-value?

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

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

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.

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.

For a sample of 100 individuals, the sample mean weekly unemployment insurance benefit was$231 with a sample standard deviation of $80. What is the p-value?

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

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

At $\alpha=.05$, 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 $\sigma$ = $\$5.60$.

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 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, $\$168,000$?

Marni Restaurant Company engaged in the following transactions during March, its first month of operations.

f. Paid employee weekly salaries of $8,500.

Required:

For each of the above business activities, indicate whether it is an operating, investing, or financing activity.

Consider the following hypothesis test:

$$\begin{array} { l } { H _ { 0 } : \mu \leq 25 } \\ { H _ { \mathrm { a } } : \mu > 25 } \end{array}$$

A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6.

What is the rejection rule using the critical value? What is your conclusion?

Consider the following hypothesis test:

$$\begin{array} { l } { H _ { 0 } : \mu \leq 25 } \\ { H _ { \mathrm { a } } : \mu > 25 } \end{array}$$

A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6.

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 dollar and 117,000 dollars, respectively. Assume the standard deviation for the male graduates is 40,000 dollars, and for the female graduates it is 25,000 dollars. a. What is the probability that a simple random sample of 40 male graduates will provide a sample mean within 10,000 dollar of the population mean, 168,000 dollars? $\newline$ b. What is the probability that a simple random sample of 40 female graduates will provide a sample mean within 10,000 dollars of the population mean, 117,000 dollars ?$\newline$ c. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within 10,000 dollars of the population mean? Why?