3. Consider the following hypothesis test:

\(\begin{aligned}

& {{H}_{0}}:{{\mu }_{1}}-{{\mu }_{2}}=0 \\

& {{H}_{A}}:{{\mu }_{1}}-{{\mu }_{2}}\ne 0 \\

\end{aligned}\)

The following results are for two independent samples taken from the two populations:

1. What is the value of the test statistic?
2. What is the \(p\) -value?
3. With \(\alpha=.05\), what is your hypothesis testing conclusion?

5. A Cornell University study of wage differentials between men and women reported that one of the reasons wages for men are higher than wages for women is that men tend to have more years of work experience than women. Assume the following results were obtained for each group.

1. What is the point estimate of the difference between the two population means?
2. At \(95 \%\) confidence, what is the margin of error?
3. What is the \(95 \%\) confidence interval estimate of the difference between the two population means?

7. During the 2003 season, Major League Baseball took steps to speed up the play of baseball games in order to maintain fan interest (CNN Headline News, September 30,2003 ). The following results come from a sample of 60 games played during the summer of 2002 and a sample of 50 games played during the summer of 2003 . The sample mean shows the mean duration of the games included in each sample.

1. A research hypothesis was that the steps taken during the 2003 season would reduce the population mean duration of baseball games. Formulate the null and alternative hypotheses.
2. What is the point estimate of the reduction in the mean duration of games during the 2003 season?
3. Historical data indicate a population standard deviation of 12 minutes is a reasonable assumption for both years. Conduct the hypothesis test and report the \(p\) -value. At a = .05 level of significance, what is your conclusion?
4. Provide a \(95 \%\) confidence interval estimate of the reduction in the mean duration of games during the 2003 season.
5. What was the percentage reduction in the mean time of baseball games during the 2003 season? Should management be pleased with the results of the statistical analysis? Discuss. Should the length of baseball games continue to be an issue in future years? Explain.

11. Consider the following data for two independent random samples taken from two normal populations.

1. Compute the two sample means.
2. Compute the two sample standard deviations.
3. What is the point estimate of the difference between the two population means?
4. What is the \(90 \%\) confidence interval estimate of the difference between the two population means?

13. FedEx and United Parcel Service (UPS) are the world's two leading cargo carriers by volume and revenue (The Wall Street Journal, January 27, 2004). According to the Airports Council International, the Memphis International Airport (FedEx) and the Louisville International Airport (UPS) are two of the ten largest cargo airports in the world. The following random samples show the tons of cargo per day handled by these airports. Data are in thousands of tons.

1. Compute the sample mean and sample standard deviation for each airport.
2. What is the point estimate of the difference between the two population means? Interpret this value in terms of the higher-volume airport and a comparison of the volume difference between the two airports.
3. Develop a \(95 \%\) confidence interval of the difference between the daily population means for the two airports.

15. Injuries to Major League Baseball players have been increasing in recent years. For the period 1992 to 2001, league expansion caused Major League Baseball rosters to increase 15%. However, the number of players being put on the disabled list due to injury increased 32% over the same period (USA Today, July 8, 2002). A research question addressed Whether Major League Baseball players being put on the disabled list are on the list longer in 2001 than players put on the disabled list a decade earlier.

1. Using the population mean number of days a player is on the disabled list, formulate null and alternative hypotheses that can be used to test the research question.
2. Assume that the following data apply:
   
   What is the point estimate of the difference between population mean number of days on the disabled list for 2001 compared to 1992 ? What is the percentage increase in the number of days on the disabled list?
3. Use \(\alpha=.01\). What is your conclusion about the number of days on the disabled list? What is the \(p\) -value?
4. Do these data suggest that Major League Baseball should be concerned about the situation?

23. Bank of America's Consumer Spending Survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries, dining out, household expenses, home furnishings, apparel, and entertainment (U.S. Airways Attaché, December 2003). Using data from a sample of 42 credit card accounts, assume that each account was used to identify the annual credit card charges for groceries (population 1) and the annual credit card charges for dining out (population 2). Using the difference data, the sample mean difference was \(\tilde{d}=\\) 850$, and the sample standard deviation was \(s_{d}=\\) 1123$.

1. Formulate the null and alternative hypotheses to test for no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.
2. Use a .05 level of significance. Can you conclude that the population means differ? What is the \(p\) -value?
3. Which category, groceries or dining out, has a higher population mean annual credit card charge? What is the point estimate of the difference between the population means? What is the \(95 \%\) confidence interval estimate of the difference between the population means?

25. In recent years, a growing array of entertainment options competes for consumer time. By 2004 , cable television and radio surpassed broadcast television, recorded music, and the daily newspaper to become the two entertainment media with the greatest usage (The Wall Street Journal, January 26,2004). Researchers used a sample of 15 individuals and collected data on the hours per week spent watching cable television and hours per week spent listening to the radio.

1. Use a .05 level of significance and test for a difference between the population mean usage for cable television and radio. What is the \(p\) -value?
2. What is the sample mean number of hours per week spent watching cable television? What is the sample mean number of hours per week spent listening to radio? Which medium has the greater usage?

29. Samples were selected from three populations. The data obtained follow.

1. Compute the between-treatments estimate of \(\sigma^{2}\).
2. Compute the within-treatments estimate of \(\sigma^{2}\).
3. At the \(\alpha=.05\) level of significance, can we reject the null hypothesis that the three population means are equal? Explain.
4. Set up the ANOVA table for this problem.

33. The Texas Transportation Institute at Texas A&M University conducted a survey to determine the number of hours per year drivers waste sitting in traffic. Of 75 urban areas studied, the most jammed urban area was Los Angeles where drivers wasted an average of 90 hours per year (U.S. News \& World Report, October 13, 2003). Other jammed urban areas included Denver, Miami, and San Francisco. Assume sample data for six drivers in each of these cities show the following number of hours wasted per year sitting in traffic.

1. Compute the sample mean hours wasted per year for each of these urban areas.
2. Using \(\alpha=.05\), test for significant differences among the population mean wasted time for these three urban areas. What is the \(p\) -value? What is your conclusion?

35. A study reported in the Journal of Small Business Management concluded that self-employed individuals experience higher job stress than individuals who are not self-employed. In this study job stress was assessed with a 15 -item scale designed to measure various aspects of ambiguity and role conflict. Ratings for each of the 15 items were made using a scale with $1-5$ response options ranging from strong agreement to strong disagreement. The sum of the ratings for the 15 items for each individual surveyed is between 15 and 75 , with higher values indicating a higher degree of job stress. Suppose that a similar approach, using a 20-item scale with 1-5 response options, was used to measure the job stress of individuals for 15 randomly selected real estate agents, 15 architects, and 15 stockbrokers. The results obtained follow.

Use \(\alpha=.05\) to test for any significant difference in job stress among the three professions.

Two Sample hypothesis test worksheet:

Purpose

This assignment will assess your ability to complete a test of independence.

Action Items

1. Complete the Two-Sample Hypothesis Tests Worksheet.
2. Using e-mail, chat rooms, or the telephone, discuss your worksheet responses with your team.

Farmer McDonald has a large cow farm. The CowChow salesperson has recently visited Old McDonald's Farm and sees it as an account worth pursuing and has claimed that the CowChow will pay off in the long run because it will make the cows put on weight faster than the current food that Old McDonald's Farm uses. Farmer McDonald is not convinced that the new cow food will make any difference in the cow weight gain and so his farm manager proposes a test. The CowChow salesperson has agreed to provide the CowChow free of charge for the test.

The manager of the farm takes two cows from each litter of cows. Carefully labeling the cows he randomly assigns one of the pair to be fed CowChow and the other to be fed on the old cow food. Since the litters were not all born at the same time the current weights of the cows vary considerably. After six months the farm manager weighs all of the cows resulting in the following:

The manager suggests that they us a two sample t-test with pooled standard deviations on this data:

1. The manager tells you to run this test. Show all steps.
2. Farmer McDonald has taken a statistics class and remembers a different test called a "paired test". He tells the manager to run the test as a paired test. Run this test on the same data and show all steps.
3. The results are obviously different. Explain which test is the better one and what circumstances resulted in the differences.
4. Discuss with Farmer McDonald your advice regarding buying the CowChow. Remember it is slightly more expensive than the current chow used.

Price: $38.62

Solution: The downloadable solution consists of 15 pages, 2362 words and 11 charts.
Deliverable: Word Document