# Testing of Hypothesis with a Student T Test

See attached file for full problem description.

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 by 15%. However, the number of players being put on the disabled list due to injury increased 32% over the same period. 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.

a. Using the population mean number of days a player is on the disabled list, formulate null and alternative hypothesis that can be used to test the research questions.

b. Assume that the following data apply:

2001 Season 1992 Season

Sample Size n = 45 n = 38

¹ ²

Sample mean _

X = 60 days _ = 51 days

x

²

Sample standard deviation s = 18 days s = 15 days

¹ ²

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?

c. Use a = .01 What is your conclusion about the number of days on the disabled list? What

is the p-value?

d. 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. 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 _ = $850, and

d

the sample standard deviation was s = $1123.

d

a. 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.

b. Use a .05 level of significance. Can you conclude that the population means differ? What

is the p-value?

c. 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. Please see excel file named tvradio

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. 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.

a. Use a .05 level if significance and test for a difference between the population mean

usage for cable television and radio. What is the p-value?

b. What is the sample 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?

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#### Solution Summary

Students t test for comparison of mean of two sets of observations. Null hypothesis, alternative hypothesis, significance level, critical value, P value are given with explanations of the results obtained.