For Exercises 47–50, do the following:

  1. Find .
  2. Determine whether the conditions are met for constructing a confidence interval for .
  3. If the conditions are met, construct and interpret a confidence interval for with the indicated confidence level, and sketch the confidence interval on the number line. If the conditions are not met, state why not.

Question 8.227

50. NASCAR Fans and Pickup Trucks. American Demographics magazine reported that 40% of a sample of NASCAR racing attendees said they owned a pickup truck. Suppose the sample size was 1000. Construct a 90% confidence interval for the population proportion of NASCAR racing attendees who own a pickup truck.