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?

Compare the U.S. Constitutional Republic to Contemporary Forms of Government Compare the U.S. constitutional republic to contemporary forms of government such as authoritarian. Compare the U.S. constitutional republic to Egypt under the Muslim Brotherhood. When writing the paragraph, answer the following questions: What was the Arab Spring? How did it start? What was the Muslim Brotherhood? How was Egypt under Muslim Brotherhood rule different from democracy in the United States?

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.

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.

Because of high production-changeover time and costs, a director of manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented. The current production method operates with a mean cost of $\$220$ per hour. A research study will measure the cost of the new method over a sample production period.

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

A business student claims that, on average, an MBA student is required to prepare more than five cases per week. To examine the claim, a statistics professor asks a random sample of 10 MBA students to report the number of cases they prepare weekly. The results are exhibited here. Can the professor conclude at the 5% significance level that the claim is true, assuming that the number of cases is normally distributed with a standard deviation of 1.5?

$$\begin{array}{llllllllll}2 & 7 & 4 & 8 & 9 & 5 & 11 & 3 & 7 & 4\end{array}$$

The following sample data are from a normal population: $10,~ 8,~12,~ 15,~ 13,~ 11,~ 6,~ 5.$ What is the point estimate of the population mean?

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $\$30,000$ and $\$45,000.$ Assume that a $95\%$ confidence interval estimate of the population mean annual starting salary is desired. What is the planning value for the population standard deviation? How large a sample should be taken if the desired margin of error is $\$200$?

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $\$30,000$ and $\$45,000$. Assume that a $95\%$ confidence interval estimate of the population mean annual starting salary is desired. What is the planning value for the population standard deviation? How large a sample should be taken if the desired margin of error is $\$100$?

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $\$ 30,000$ and $\$ 45,000$. Assume that a $95 \%$ confidence interval estimate of the population mean annual starting salary is desired. What is the planning value for the population standard deviation? How large a sample should be taken if the desired margin of error is

$\$ 500$ ?

$\$ 200$ ?

$\$ 100$ ?

Would you recommend trying to obtain the $\$ 100$ margin of error? Explain.

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $\$ 30,000$ and $\$ 45,000$. Consider that a $95 \%$ confidence interval estimate of the population mean annual starting salary is desired.

c. Would you recommend trying to obtain the $\$ 100$ margin of error? Explain.

$Playbill$ magazine reported that the mean annual household income of its readers is $\$119,155$ ($Playbill$, January $2006$). Assume this estimate of the mean annual household income is based on a sample of $80$ households, and based on past studies, the population standard deviation is known to be $\sigma=\$30,000.$

Develop a $90\%$ confidence interval estimate of the population mean.

The Wall Street Journal reported that automobile crashes cost the United States $\$ 162$ billion annually (The Wall Street Journal, March 5, 2008). The average cost per person for crashes in the Tampa, Florida, area was reported to be $\$ 1599$. Suppose this average cost was based on a sample of 50 persons who had been involved in car crashes and that the population standard deviation is $\sigma=\$ 600$. What is the margin of error for a $95 \%$ confidence interval? What would you recommend if the study required a margin of error of $\$ 150$ or less?

In an effort to estimate the mean amount spent per customer for dinner at a major Atlanta restaurant, data were collected for a sample of $49$ customers. Assume a population standard deviation of $\$5.$

At $95\%$ confidence, what is the margin of error?

$BusinessWeek$ 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, $\$168,000$?