Estimation of Unknown Parameters

Show all your work (or calculator comments) in answering following questions.

Problem 1: Age of residents

A condo community management in Florida wants to improve the amenities they provide for their tenants. In order to make a more appealing selection of amenities, they want to estimate the mean age of the people who reside in that community. Based on this estimation they will decide, for example, whether to offer a free one year membership to a gym, or a free one year membership to a fruit-of the-month club. The manager takes a random sample of 50 residents from this community and records their ages. The data listed as follows.

27	37	42	48	56	61	65	68	72	79
30	37	45	50	58	61	65	69	75	83
32	39	46	53	59	62	65	69	75	87
34	40	47	56	61	62	66	70	76	91
36	40	47	56	61	62	66	71	77	95

1. What is the point estimate for the mean age of all residents in this condo community? Use the correct symbol to report your answer.

1. Construct an 85% confidence interval to estimate the mean age of all residents in this community.

1. Construct a 95% confidence interval to estimate the mean age of all residents in this community.

1. Construct a 99% confidence interval to estimate the mean age of all residents in this community.

1. Compare the three intervals you got above. Explain how increasing the confidence level changed the margin of error of each interval. Do the intervals get wider or smaller as the confidence levels increase?

Problem 2: Online Books

A consumer research center surveyed 427 randomly selected women and found that 29% of them purchase books online.

1. What is the number of women in this sample who said that they purchase books online? Round to the nearest integer.

1. Find a 95% confidence interval estimate of the percentage of all women who purchase books online.

1. Can we safely conclude that less than 40% of all women purchase books online? Why or why not?

1. Can we safely conclude that at least 25% of all women purchase books online? Why or why not?

1. Suppose the consumer research center researchers wanted to be 95% confident that their estimate is within 2% of the true population proportion. How large a sample should they select for their survey? Use the preliminary estimate given in their first survey stated in the problem above.

Problem 3: Find the Sample Size

A researcher wishes to be 95% confident that her estimate of the true proportion of individuals who travel overseas is within 4% of the true proportion. If there is no preliminary estimate available, how large should the sample be?

Problem 4: Drill Time

A sample of 50 drills had a mean lifetime 12.68 holes drilled when drilling a low-carbon steel. Assume the population standard deviation is 6.83 holes drilled.

a. Calculate the 99% confidence interval for the population mean number of holes drilled by these drills.

Find the margin of error:

b. Now suppose a sample of 80 drills has a mean lifetime 12.68 holes drilled when drilling a low-carbon steel. Assume the population standard deviation is 6.83 holes drilled. Calculate the 99% confidence interval for the population mean number of holes drilled by these drills.

Find the margin of error:

What do you notice about the margin of error as the sample size increases?

Pre - Lab Activity: TI-83/84 Confidence Intervals

You can use the TI-83/84 calculator to calculate confidence intervals for population means (both when