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.
- A survey of 30 adults found that the mean age of a person’s primary vehicle is 5.7 years. Assuming the standard deviation of the population is 0.9 year:
- Find the 98% confidence interval of the population mean.
- Interpret your findings.
- The manager of a bank that has 1,000 depositors wants you to estimate the proportion of its depositors with more than one account at the bank. A random sample of 100 depositors is selected, and 30 state that they have more than one account at the bank.
- Construct a 90% confidence interval estimate of the population proportion of the bank’s depositors who have more than one account at the bank.
- Interpret the interval estimate.
- Given the margin of error in (a), what sample size is needed to estimate the population proportion to within with 90% confidence?
- An automobile shop manager timed six employees and found that the average time it took them to change a water pump was 19 minutes and he standard deviation was 3.5 minutes. Assuming a normal population:
- Find the 99% confidence interval of the true mean.
- Interpret the interval estimate.
- A restaurant owner wishes to find the 99% confidence interval of the true mean cost of a dry martini. How large should the sample be if she wishes to be accurate within $0.20? A previous study showed that the standard deviation of the price was $0.15.
- A recent study of 30 city residents showed that the mean of the time they had lived at their present address was 9.5 years and the standard deviation was 3 years. Assuming a normal population:
- Find the 90% confidence interval of the true mean.
- Interpret the interval estimate.
- A US Travel Data Center survey conducted for Better Homes and Gardens of 1600 adults found that 40% said that they would take more vacations this year than last year.
- Find the 90% confidence interval for the true proportion of adults who said that they will travel more this year.
- Interpret the interval estimate.
