Question

I recommend that you practice using the standard Normal tables to calculate zα/2 and tα/2 .

1. Costs are rising for all kinds of health care. The mean monthly rent at assisted-living facilities was recently reported to have increased 15% over the last five years. A recent random sample of 120 observations reported a sample mean of $3563. Assume that past studies have informed us that the population standard deviation is $650.

For this problem, round your answers to 2 digits after the decimal point.

1. (a) What are the end points of a 90% confidence-interval estimate for the mean monthly rent in the population?

2. (b) What are the end points of a 95% confidence-interval estimate for the mean monthly rent in the population?

3. (c) What are the end points of a 99% confidence-interval estimate for the mean monthly rent in the population?

2. Sometimes we do not want one of the usual confidence levels. What is zα/2, when the confidence level is 75.8%?

For this problem, round your answers to 3 digits after the decimal point.

3. Customer satisfaction is measured on a scale between -2 and 2. The last survey estimated mean customer satisfaction to be .41 with a known standard deviation of 4.46. Another survey is going to be taken. Given past results, you really need to have a margin of error of .19 in your 95% confidence interval. What is the smallest sample size that will get you this margin of error?

4. Sometimes we want a confidence level using the t distribution What is tα/2, when there are 21 degrees of freedom and the confidence level is 98%?

For this problem, round your answers to 3 digits after the decimal point.

5. The U.S Census has estimated the percentages of the U.S population that have achieved differ- ent levels of education. See https://factfinder.census.gov/faces/tableservices/jsf/ pages/productview.xhtml?src=CF for some of the estimates. This question uses numbers inspired by these results.

Suppose that the sample proportion for the U.S. population aged between 25 and 34 years that has a Bachelors’s degree or higher is .34. Further suppose that this estimate came from a survery of 1461 people.

(a) What are the end points of a 90% confidence interval estimate for the population pro- portion? (Round to 2 digits after the decimal place.)

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(b) What are the end points of a 95% confidence interval estimate for the population pro- portion? (Round to 2 digits after the decimal place.)

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(c) What are the end points of a 99% confidence interval estimate for the population pro- portion? (Round to 2 digits after the decimal place.)

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6. The American Time-Use Survey uses surveys to estimate how much time people in the U.S. spend doing various activities. See https://www.bls.gov/news.release/pdf/atus.pdf for some recent estimates. The numbers in this question are inspired by these results.

We want to know the mean number of hours worked on a weekend day, among those who work weekends. Suppose that a simple random sample of size 1028 from the target population produced a sample mean of 5.1 hours. Further suppose that the sample standard deviation was 2.2.

1. (a) What are the end points of a 90% confidence-interval estimate for the population mean? (Round to 2 digits after the decimal place.)

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2. (b) What are the end points of a 95% confidence-interval estimate for the population mean? (Round to 2 digits after the decimal place.)

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3. (c) What are the end points of a 99% confidence-interval estimate for the population mean? (Round to 2 digits after the decimal place.)

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Answer 1