Question 8.140

43. Consumer Sentiment. The University of Michigan Surveys of Consumers found that the mean index of consumer sentiment for December 2013 was 82.5. Suppose this result was based on a sample of size 100, which had a standard deviation of 10.

  1. State how the conditions for the interval for are met.
  2. Find for a confidence interval with 95% confidence.
  3. Construct and interpret a 95% confidence interval for the population mean consumer sentiment.

8.2.43

(a) We are not told that the population is normal. However, the sample size is large ( is ). (b) (c) (80.5, 84.5). We are 95% confident that μ, the population mean consumer sentiment for all consumers, lies between 80.5 and 84.5.