Confidence Intervals

Explain the purpose and dynamics of confidence intervals.

1. In a study of 27 criminals convicted of antitrust offenses, the average age was 52 years, with a standard deviation of 7.3 years. Construct a 98% confidence interval for the true mean age of these type of offenders in the general population. (Give your answers correct to one decimal place.)

Lower =

Upper =

1. A company has a new process manufacturing large artificial sapphires. In a trial run, 46 sapphires are produced. The distribution of weights is mound-shaped and symmetric. The mean for these 46 gems is x-bar = 8.32 carats, and the sample standard deviation is .33. Let be the mean weight for the distribution of all sapphires produced by the new process. [This is based on the Guided Exercise from p. 379 in the B & B text.]
2. Does the sample meet the requirements needed to compute confidence intervals? Explain.
3. Calculate the 95% confidence interval. Is the population s.d. given? Based on this answer which test-statistics will you use to do the calculation?
4. What does the confidence interval tell us in context to the problem?