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?

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?

The average annual total return for U.S. Diversified Equity mutual funds from 1999 to 2003 was 4.1% (BusinessWeek, January 26, 2004). A researcher would like to conduct a hypothesis test to see whether the returns for mid-cap growth funds over the same period are significantly different from the average for U.S. Diversified Equity funds.

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

The U.S. Department of Labor reported the average hourly earnings for U.S. production workers to be $14.32 per hour in 2001 (The World Almanac, 2003). A sample of 75 production workers during 2003 showed a sample mean of$14.68 per hour. Assuming the population standard deviation $\sigma$= $1.45, can we conclude that an increase occurred in the mean hourly earnings since 2001? Use$\alpha$= .05.

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).

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

The U.S. Department of Labor found that the unemployment rate for Germany was 5.0% in 1990 and 9.3% in 2003. Determine the approximate average annual rate of increase in unemployment for these 13 years.

Find the margin of error and the $95 \%$ confidence interval for the following studies. Briefly interpret the $95 \%$ confidence interval.

A recent survey of $65,000$ households by the U.S. Department of Labor reported an unemployment rate of $7.7 \%$.

The average annual total return for U.S. Diversified Equity mutual funds from 1999 to 2003 was 4.1% (BusinessWeek, January 26, 2004). A researcher would like to conduct a hypothesis test to see whether the returns for mid-cap growth funds over the same period are significantly different from the average for U.S. Diversified Equity funds.

Formulate the hypotheses that can be used to determine whether the mean annual return for mid-cap growth funds differ from the mean for U.S. Diversified Equity funds.

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.

Trading volume on the New York Stock Exchange is heaviest during the first half hour (early morning) and last half hour (late afternoon) of the trading day. The early morning trading volumes (millions of shares) for 13 days in January and February are shown here (Barron’s, January 23, 2006; February 13, 2006; and February 27, 2006).

$$\begin{matrix} \text{214} & \text{163} & \text{265} & \text{194} & \text{180}\\ \text{202} & \text{198} & \text{212} & \text{201}\\ \text{174} & \text{171} & \text{211} & \text{211}\\ \end{matrix}$$

The probability distribution of trading volume is approximately normal.

What is the probability that, on a randomly selected day, the early morning trading volume will be less than 180 million shares?

Wall Street securities firms paid out record year-end bonuses of $125,500 per employee for 2005 (Fortune, February 6, 2006). Suppose we would like to take a sample of employees at the Jones & Ryan securities firm to see whether the mean year-end bonus is different from the reported mean of$125,500 for the population.

State the null and alternative hypotheses you would use to test whether the year-end bonuses paid by Jones & Ryan were different from the population mean.

Wall Street securities firms paid out record year-end bonuses of $125,500 per employee for 2005 (Fortune, February 6, 2006). Suppose we would like to take a sample of employees at the Jones & Ryan securities firm to see whether the mean year-end bonus is different from the reported mean of$125,500 for the population.

With $\alpha$ = .05 as the level of significance, what is your conclusion?

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?

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