CBESTA2 Exercises - Announcements



STATSCI Exercises

Estimation of Parameters

1. In a random sample of n = 500 families owning television sets in the city of Hamilton, Canada, it was found that x = 340 subscribed to HBO. Find a 95% confidence interval for the actual proportion of families in this city who subscribe to HBO. How large a sample would be needed if we do not wish our error to exceed 0.02 at 95% confidence?

2. A random sample of n = 200 students were selected and it was found that 114 prefer Adidas over other sports brands.

a. Find a 95% confidence interval for the actual proportion of students who prefer Adidas.

a. How large a sample is needed if we want to be 95% confident that the error will not exceed 0.15?

3. Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 65 weekly reports showed a sample mean of 19.5 customer contacts per week. The sample standard deviation was 5.2. Provide 90% and 95% confidence intervals for the population mean number of weekly customer contacts for the sales personnel.

4. Bride’s magazine reported that the mean cost of a wedding is $19,000. Assume that the population standard deviation is $9400. Bride’s plans to use an annual survey to monitor the cost of a wedding. Use 95% confidence.

a. What is the recommended sample size if the desired margin of error is $1000?

b. What is the recommended sample size if the desired margin of error is $500?

c. What is the recommended sample size if the desired margin of error is $200?

5. The contents of 7 similar containers of sulfuric acid are 9.8, 10.2, 10.4, 9.8, 10.0, 10.2, and 9.6 liters. Find a 95% confidence interval for the mean content of all such containers, assuming an approximate normal distribution for container contents.

6. Gasoline prices increased substantially from 1999 to 2000. The American Automobile Association provided information on the mean cost per gallon for self-serve regular unleaded gasoline over the 2 years. Assume the following results were obtained from independent samples of locations throughout the country.

Suppose the mean cost in 2000 was computed to be $1.58 with a standard deviation of $0.12 (obtained from 50 samples) while the mean cost in 1999 was $0.98 with a standard deviation of $0.08 (obtained from 42 samples).

Provide a 95% confidence interval estimate of the increase in the mean cost per gallon from 1999 to 2000.

7. The international Air Transport Association surveyed business travelers to determine ratings of various international airports. The maximum possible rating score was 10. Suppose 50 business travelers were asked to rate the Miami airport, and 50 other business travelers were asked to rate the Los Angeles airport. The rating scores follow.

Miami

4 6 8 7 7 6 3 3 8 10 4 8 7 8 7 5 9 5 8 4 3 8 5 5 4 4 4 8 4 5 6 2 5 9 9 8 4 8 9 9 5 9 7 8 3 10 8 9 6 6

Los Angeles

10 9 6 7 8 7 9 8 10 7 6 5 7 3 5 6 8 7 10 8 4 7 8 6 9 9 5 3 1 8 9 6 8 5 4 6 10 9 8 3 2 7 9 5 3 10 3 5 10 8

Develop a 95% confidence interval estimate of the difference between the mean ratings of the Miami and Los Angeles airports.

8. 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 than men tend to have more years of work experience than women. Assume the following sample summaries show the years of experience for each group.

Men Women

[pic]years [pic] years

[pic]years [pic]years

[pic] [pic]

What is the 95% confidence interval estimate of the difference between the two population means.

9. An urban planning group is interested in estimating the difference between the mean household incomes for two neighborhoods in a large metropolitan area. Independent random samples of households in the neighborhoods provided the following results.

[pic]

Develop a 95% confidence interval for the difference between the mean incomes in the two neighborhoods.

10. The National Association of Home Builders provided data on the cost of the most popular home remodeling projects. Sample data on cost (in thousands of dollars) for the two types of remodeling projects are as follows.

Kitchen

25.2 17.4 22.8 21.9 19.7 23.0 19.7 16.9 21.8 23.6

Master Bedroom

18.0 22.9 26.4 24.8 26.9 17.8 24.6 21.0

Develop a 90% confidence interval for the difference between the two population means.

11. A poll is taken among the residents of a city and the surrounding county to determine the feasibility of a proposal to construct a civic center. If 2400 of 5000 city residents favor the proposal and 1200 of 2000 county residents favor it, find a 90% confidence interval for the true difference in the fractions favoring the proposal to construct the civic center.

12. A geneticist is interested in the proportion of males and females in the population that have a certain minor blood disorder. In a random sample of 100 males, 24 are found to be afflicted, whereas 13 of 100 females tested appear to have the disorder. Compute a 99% confidence interval for the difference between the proportion of males and females that have this blood disorder.

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