Statistics: Problems and Solutions

1. A sample of 35 golfers showed that their average score on a particular golf course was 80 with a standard deviation of 6.
Answer each of the following (show all work):
(A) Find the 95% confidence interval of the mean score for all 35 golfers.
(B) Find the 95% confidence interval of the mean score for all golfers if this is a sample of 50 golfers instead of a sample of 35.
(C) Which confidence interval is smaller and why?

2. A researcher is interested in estimating the noise levels in decibels at area urban hospitals. She wants to be 90% confident that her estimate is correct. If the standard deviation is 4.8, how large a sample is needed to get the desired information to be accurate within 0.70 decibels? Show all work.

3. A researcher claims that the average age of people who buy lottery tickets is 60. A sample of 30 is selected and their ages are recorded as shown below. The standard deviation is 15. At α = 0.01 is there enough evidence to reject the researcher's claim? Show all work.
65 63 75 52 22 80 72 56 82 56
24 60 70 74 70 61 65 71 39 74
79 75 71 49 62 68 71 67 69 45

4. Given a level of confidence of 99% and a population standard deviation of 10, what other information is necessary:
(A) To find the Maximum Error of Estimate (E)?

(B) To find the sample size (n)?

(C) Given the above confidence level and population standard deviation, find the Maximum Error of Estimate (E) if n = 45. Show all your calculations. Show all work.

(D) For this same sample of n = 45, what is the width of the confidence interval around the population mean? Show all work.

(E) Given this same confidence level and standard deviation, find n if E = 3.5. (Always round to the nearest whole person.)

5. By measuring the amount of time it takes a component of a product to move from one workstation to the next, an engineer has estimated that the standard deviation is 4.0 seconds.
Answer each of the following (show all work):
(A) How many measurements should be made in order to be 95% certain that the maximum error of estimation will not exceed 1 second?

(B) What sample size is required for a maximum error of 2 seconds?

6. A 95% confidence interval estimate for a population mean was computed to be (44.8 to 50.2). Determine the mean of the sample, which was used to determine the interval estimate (show all work).

7. A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having two children. A sample of 130 was taken, and the mean amount spent was $190. Assuming a standard deviation equal to $40, find the 95% confidence interval for μ, the mean for all such families (show all work).

8. Write a correct null and alternative hypothesis for testing the claim that the mean life of a battery for a cell phone is at least 65 hours.

9. Write a correct alternative hypothesis that tests the claim that the mean distance a student commutes to campus is no less than 6.4 miles?