Week 9: Homework Assignment 5

Homework Assignment #5.

Instructions: Show your solutions using PhStat/Excel or manual calculations. You can take a screenshot of your PhStat solutions here or submit an Excel file with all your answers to each question. You must clearly label your final answers. Solutions and final answers are separately graded.

1. According to a recent survey of 50 adults, it was found that the average age of their automobiles is 12.6 years old. Assuming the standard deviation of the population is 2.1 years:

1. Find the 90% confidence interval of the population mean.

1. Interpret your findings.

2. A local bank currently has2,000 depositors and its manager wants you to estimate the proportion of its depositors with multiple accounts at the bank. A random sample of 200 depositors is selected, and 50 indicate that they have multiple accounts at the bank.

1. Construct a 90% confidence interval estimate of the population proportion of the bank’s depositors with multiple accounts at the bank.

1. Interpret the interval estimate.

1. Given the margin of error in (a), what sample size is needed to estimate the population proportion to within with 95% confidence?

3. A local Pep Boys timed its eight employees and found that it took them an average of 15 minutes to perform an oil change with a standard deviation of 3 minutes.

1. Construct a 95% confidence interval for the true mean.

1. Interpret the interval estimate.

4. A restaurant owner wishes to find the 95% confidence interval of the true mean cost of a dry martini. How large should the sample be if she wishes to be accurate within $0.25? A previous study showed that the standard deviation of the price was $0.2.

5. The American Camp Association (ACA) conducted a survey among 1500 children aged 10 to 15 and found out that only 25% would be participating in this year’s summer camp.

1. Find the 95% confidence interval for the true proportion of those participating in this yea’r summer camp.

1. Interpret the interval estimate.

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