Question

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.

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

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

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

5. 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?

Answer 1

a) The point estimate of the mean is the sample mean

b)

c)

d)

e) As the confidence level increases the interval gets wider.

Increasing the confidence level increases the error bound, making the confidence interval wider.