1. Apartment rental rates. You want to rent an unfurnished one-bedroom apartment for next semester. The mean monthly rent for a random sample of 10 apartments advertised in the local newspaper is $540. Assume that the standard deviation is $80. Find a 95% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community.
  2. Compare the margin of error for intervals with 90, 95, and 99% confidence:
  3. Suppose you desire a 90% confidence interval with a width of no more than $50. What sample size is needed?
  1. Clothing for runners. Your company sells exercise clothing and equipment on the Internet. To design the clothing, you collect data on the physical characteristics of your different types of customers. Here are the weights (in kilograms) for a sample of 24 male runners. Suppose the standard deviation of the population is known to be 4.5 kg.

67.8 61.9 63.0 53.1 62.3 59.7 55.4 58.9 60.9 69.2 63.7 68.3 64.7
65.6 56.0 57.8 66.0 62.9 53.6 65.0 55.8 60.4 69.3 61.7

  1. What is the standard deviation of x-bar?
  2. Give a 95% confidence interval for µ, the mean of the population from which the sample is drawn. (The sample mean is 61.79, to save you some time).
  3. Will the interval contain the weights of approximately 95% of all similar runners? Explain.
  1. 99% versus 95% confidence interval. Find a 99% confidence interval for the mean weight µ of the population of male runners in Exercise 6.12 (with n=24). Is the 99% confidence interval wider or narrower than the 95% interval found in Exercise 6.12? Explain in plain language why this is true.
  2. Suppose you want the 99% interval to be the same width as the 95% interval. How many additional runners would you need to include in your sample?
  1. A company that produces white bread is concerned about the distribution of the amount of sodium in its bread. The company takes a simple random sample of 100 slices of bread and computes the sample mean to be 103 milligrams of sodium per slice.
  2. Construct a 99% confidence interval for the unknown mean sodium level assuming that the population standard deviation is 10 milligrams.
  3. Interpret the 99% confidence interval found in (a).
  4. You work for a consumer advocate agency and want to find the mean repair cost of a washing machine. In the past, the standard deviation of the cost of repairs for washing machines has been $17.50. As part of your study, you randomly select 40 repair costs and find the mean to be $100.00.
  5. Calculate a 90% confidence interval for the population mean.
  1. Interpret the interval found in (a).
  1. The actual time it takes to cook a 10 – pound turkey is a normal random variable with a mean of 2.8 hours and a standard deviation of 0.24 hours. Suppose that a random sample of 35 10 – pound turkeys is taken.
  2. What is the probability that a randomly selected 10-pound turkey will take less than 3.1 hours to cook?
  3. What is the probability that the average cooking time of a 10 – pound turkey will take between 2.7 and 2.95 hours to cook?
  4. Given that an average of 2.9 hours was found for a sample of 35 turkeys, calculate an 80% confidence interval for the average cooking time of a 10 – pound turkey.
  5. Interpret the interval found in (c).
  6. Is the parameter that you are trying to estimate in (d) actually in the interval? What is the parameter?