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?

A class survey in a large class for first-year college students asked, "About how many hours do you study during a typical week?" The mean response of the 463 students was $\bar{x}$ = 13.7 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation $\sigma$ = 7.4 hours in the population of all first-year students at this university.

(a) Use the survey result to give a 99% confidence interval for the mean study time of all first-year students.

(b) What condition not yet mentioned must be met for your confidence interval to be valid?

A class survey in a large class for first-year college students asked, "About how many minutes do you study on a typical weeknight?" The mean response of the 463 students was $\bar{x}=118$ minutes. Suppose that we know that the study time follows a Normal distribution with standard deviation $\sigma=65$ minutes in the population of all first-year students at this university.

(a) Use the survey result to give a 99% confidence interval for the mean study time of all first-year students. (b) What condition not yet mentioned must be met for your confidence interval to be valid?

A random sample of 80 observations results in 50 successes.

a. Construct the 95% confidence interval for the population proportion of successes.|

b. Construct the 95% confidence interval for the population proportion of failures.

Athletes performing in bright sunlight often smear black eye grease under their eyes to reduce glare. Does eye grease work? In one study, 16 student subjects took a test of sensitivity to contrast after three hours facing into the bright sun, both with and without eye grease. (Greater sensitivity to contrast improves vision and glare reduces sensitivity to contrast.) This is a matched pairs design. Here are the differences in sensitivity, with eye grease minus without eye grease:

$$\begin{array}{rrrrrrrr} 0.07 & 0.64 & -0.12 & -0.05 & -0.18 & 0.14 & -0.16 & 0.03 \\ 0.05 & 0.02 & 0.43 & 0.24 & -0.11 & 0.28 & 0.05 & 0.29 \end{array}$$

We want to know whether eye grease increases sensitivity to contrast on average. Do the data support this idea? Complete the Plan, Solve, and Conclude steps of the four-step process, following the model of the given example.

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.

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 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.

Athletes performing in bright sunlight often smear black grease under their eyes to reduce glare. Does eye black work? In one experiment, 16 randomly selected student subjects took a test of sensitivity to contrast after 3 hours facing into bright sun, both with and without eye black. Here are the differences in sensitivity, with eye black minus without eye black:

$$\begin{array}{rrrrrrr} 0.07 & 0.64 & -0.12 & -0.05 & -0.18 & 0.14 & -0.16 & 0.03 \\ 0.05 & 0.02 & 0.43 & 0.24 & -0.11 & 0.28 & 0.05 & 0.29 \end{array}$$

We want to know whether eye black increases sensitivity on the average. State hypotheses. Be sure to define the parameter.

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.

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?

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?