Assignment:
Instructions
Please complete all of the following problems. You must ensure that the assignment you turn in is arranged so that all problems are in the same order as they are assigned. The assignment files must include image files (i.e. jpg, bmp, png, etc.). They must be named and formatted as explained in the Formatting Assignments page under Course Documents. You should familiarize yourself with the TI83/84 ZInterval and TInterval commands and review FAQ 4.8 and 4.10 before doing this assignment.
Rounding. Please observe the rounding guidelines in FAQ 4.2.
Expressing confidence intervals. You should express a confidence interval using interval notation (a, b), where a is the lower bound and b is the upper bound (FAQ 4.8).
Problems:
Section .1
1. Select the letter which represents the most suitable answer.Which statistic is the best unbiased estimator for µ?
(a) s
(b) x
(c) the median
(d) the mode
2. Suppose µ = 48.12 and x = 46.56. What is the sampling error?
3. Let c = 0.95, s = 3.0, and n = 60. What is the margin of error, E?
Use the confidence interval (3.144, 3.176) to answer questions 4 and 5.
4. What is the margin of error, E?
5. What is the sample mean, x?
6. Let c = 0.95, s = 2.5, and E = 1. What is the minimum sample size, n, needed to estimate µ?
7. Repair Costs: Refrigerators In a random sample of 60 refrigerators, the mean repair cost was $150.00 and the standard deviation was $15.50. Construct a 99% confidence interval forthe population mean repair cost.
Section .2
8. Let c = 0.95 and n = 12. Find the critical value, tc.
9. Let c = 0.99, s = 3, and n = 6. Find the margin of error, E.
10. Let c = 0.95, x = 13.4, s = 0.85, and n = 8. Construct a confidence interval for the population mean µ using the t-distribution.
Use the information below to answer questions 11 and 12.
Repair Costs: Computers In a random sample of 7 computers, the mean repair cost was $100.00 and the standard deviation was $42.50. Assume the repair cost is normally distributed.
11. Use a t-distribution to construct a 95% confidence interval for the population mean µ.
12. What is the margin of error, E, of µ?
Use the information below to answer questions 13-15.
Economics The monthly incomes for 14 randomly selected people, each with a bachelor's degree in economics. Assume that the population of the monthly incomes is normally distributed.
5418.76 5278.63 5912.05 6118.35 5647.86 5714.38 5365.19
5524.91 5761.57 4924.16 5494.66 5619.74 6205.64 5810.23
13. What is the sample mean, x?
14. What is the sample standard deviation, s?
15. Construct a 99% confidence interval for the population mean µ.
Section .3
Use the information below to answer questions 16 and 17.
Let p be the population proportion for the given condition.
Charity In a survey of 2939 U.S. adults, 2439 say they have contributed to a charity in the past 12 months.
16. What is the point estimate, pˆ, for p?
17. What is the point estimate, qˆ, for q?
Use the information below to answer questions 18 and 19.
Let p be the population proportion for the given condition.
Vacation In a survey of 1003 U.S. adults, 110 say they would go on vacation to Europe if cost did not matter.
18. What is the point estimate, pˆ, for p?
19. What is the point estimate, qˆ, for q?
Use the information below to answer questions 20-22. For this problem, round your results to 3 decimal places.
Charity In a survey of 2939 U.S. adults, 2439 say they have contributed to a charity in the past 12 months.
20. Construct the 95% confidence interval for the population proportion p.
21. Construct the 99% confidence interval for the population proportion p.
22. Which interval is wider?
Use the information below to answer questions 23 to 25.
Online Service Usage You are a travel agent and wish to estimate, with 98% confidence, the proportion of vacationers who use an online service or the internet to make travel reservations. Your estimate must be accurate to within 4% of the population proportion. (Note: For this problem, do not use the nearest c value in the table to approximate the solution. You must use the characteristics of c to find the correct zc value for a 98% level of confidence.)
23. No preliminary estimate is available. Find the minimum sample size needed.
24. Find the minimum sample size needed, using a prior study that found that 30% of the respondents said they used an online service or the internet to make travel reservations.
25. What do conclude from the results found in questions 23 and 24?