Intro to Calc/Stats – Chapter 6 TestName: ______

If you want me to consider partial credit, you must show your work.

77 total points

  1. (4 pts) Find the critical value for a sample of 42 and an 80% confidence level.
  1. (4 pts) Find the critical value for a sample of 10 and a 90% confidence level.
  1. (6 pts) Find the critical values, and for a sample of 15 and a 90% confidence level.
  1. (5 pts) In a random sample of 6 microwave ovens, the sample mean repair cost was $90.00 and the sample standard deviation was $13.50. Find the margin of error needed to construct a 90% confidence interval for the population mean.
  1. (5 pts) A biologist reports a confidence interval of (3.3, 4.9) when estimating the mean height (in centimeters) of a sample of seedlings. Find the sample mean and the margin of error.
  1. (5 pts) People were polled on how many books they read the previous year. How many subjects are needed to estimate the number of books read the previous year within one book with 99% confidence? Assume that books.
  1. (5 pts) If all other quantities remain the same, how does an increase in sample size affect the width of a confidence interval? Answer by choosing the appropriate phrase to fill-in-the-blank.

An increase in sample size ______the confidence interval.

a)Does not changeb) will narrow c) will widen

  1. (5 pts) In a survey of 1113 adults in Ohio, 983 said that they did not trust their state politicians. Construct, with 99% confidence, a confidence interval for the population proportion.
  1. (8 pts) A magazine includes a report on the energy costs per year for 32-inch liquid crystal display (LCD) televisions. The article states that 14 randomly selected 32-inch LCD televisions have a sample standard deviation of $3.54.

a)Construct a 95% confidence interval for the population variance. AND interpret the results.

b)Construct a 95% confidence interval for the population standard deviation. AND interpret the results.

  1. (5 pts) Many investors choose mutual funds as a way to invest in the stock market. The mean annual rate of return for mutual funds in a recent year was estimated by taking a random sample of 44 mutual funds. The mean annual rate of return for the sample was 14.73%, with a standard deviation of 7.23%. Find the confidence interval for a 95% confidence level.
  1. (6 pts) You randomly select and measure the contents of 10 bottles of cough syrup. The results (in fluid ounces) are shown. Construct 95% confidence intervals for both the population variance and standard deviation .

4.2184.2934.2584.2474.186

4.2864.2614.2484.2224.239

  1. (8 pts) You wish to estimate, with 90% confidence, the population proportion of US adults who made one or more emergency room visits in the past year. Your estimate must be accurate within 3% of the population proportion.

a) No preliminary estimate is available. Find the minimum sample size needed.

b) Find the minimum sample size needed, using a prior study that found that 12.1% of US adults made one or more emergency room visits in the past year.

  1. (6 pts) The SAT scores of 12 randomly selected high school seniors are shown below:

170419401518200514321872199816581825167022101380

Construct a 99% confidence interval for the mean SAT score of all high school seniors.

  1. (5 pts) In a random sample of 50 people, the mean body mass index (BMI) was 27.7 and the standard deviation was 6.12. Construct a 95% confidence interval for the population mean.