10.The following table gives information on ages and cholesterol levels for a random sample of 10 men.

Age58694339635247317436

Cholesterol level189235193177154191213165198181

a.Taking age as an independent variable and cholesterol level as a dependent variable, compute  the estimated regression line.

b.Interpret the slope of the regression line.

c.Predict the cholesterol level of a 60-year old man.

According to the Youth Risk Behavior Surveillance 2001 survey by the Centers for Disease Control and Prevention, 33.4% of the 9th-grade girls and 35.9% of the 12th-grade girls considered themselves overweight. Assume that these percentages are based on random samples of 750 ninth-grade and 738 twelfth-grade girls.

a.Determine a 99% confidence interval for the difference between the two population proportions.

b.At the 1% significance level, can conclude that the proportion of all 9th-grade girls who consider themselves overweight is less than the proportion of all 12th-grade girls who think they are overweight?

A company sent seven of its employees to attend a course in building self-confidence. These employees were evaluated for their self-confidence before and after attending this course. The following table gives the scores (on a scale of 1 to 15, 1 being the lowest and 15 being the highest score) of these employees before and after they attended the course.

Before8549695

After108511679

Assume that the population of paired differences has a normal distribution.

a.Construct a 95% confidence interval for the mean d of the population paired differences, where a paired difference is equal to the score of an employee before attending the course minus the score of the same employee after attending the course.

b.Test at the 1% significance level whether attending this course increases the mean score of employees.

A company claims that its medicine, Brand A, provides faster relief from pain than another company's medicine, Brand B. A researcher tested both brands of medicine on two groups of randomly selected patients. The results of the test are given in the following table. The mean and standard deviation of relief times are in minutes.

Brand
Sample SizeMean of
Relief TimesStandard Deviation
Of Relief Times
A254411
B22499

Assume that the two populations are normally distributed with unequal standard deviations.

a.Construct a 99% confidence interval for the difference between the mean relief times for the  two brands of medicine.

b.Test at the 1% significance level whether the mean relief time for Brand A is less than that for Brand B.

The department of labor in a state wanted to find the compensation of hotel employees. A random sample of 20 cleaning persons produced the mean hourly earnings (including tips) of $10.60 with a standard deviation of $1.02. a random sample of 25 bellhops gave the mean hourly earnings (including tips) of $11.57 with a standard deviation of $1.34. Assume that the hourly earnings of both groups are normally distributed with equal but unknown population standard deviations.

a.Construct a 99% confidence interval for the difference between the corresponding population means of the two groups.

b.Using the 5% significance level, can you conclude that the mean hourly earnings of all cleaning persons are lower than those of all bellhops in this state?

According to the Employment Policy Foundation's seventh annual report, titled Challenges Facing the American Workplace, women held 49% of management and professional jobs in 2000 (The Hartford Courant, September 2, 2002). Suppose that a recent random smaple of 200 such jobs found that 52% of these are held by women. Can you conclude that the percentage of such jobs that are held by women currently exceeds 49%? Use = .025. Calculate the p-value and do the problem using the p-value approach.

A past study claims that adults in America spend an average of 18 hours a week on leisure activities. A researcher wanted to test this claim. she took a sample of 10 adults and asked them about the time they spend per week on leisure activities. Their responses (in hours) are as follows.

14252238162619234133

Assume that the times spent on leisure activities by all adults are normally distributed. Using the 5% significance level, can you conclude that the claim of the earlier study is true?

According to a survey by the National Retail Association, the average amount that households in the United States planned to spend on gifts, decorations, greeting cards, and food during the 2001 holiday season was $940 (Money, December 2001). Suppose that a recent random sample of 324 households showed that they plan to spend an average of $1005 on such items during this year's holiday season with a standard deviation of $330. Test at the 1% significance level whether the mean of such planned holiday-related expenditures for households for this year differs from $940. Do the problem using the critical value approach and the p-value approach.