3. Estimate Interval The makers of a soft drink want to identifythe average age of its consumers. A sample of 61 consumers wastaken. The average age in the sample was 23 years with a samplestandard deviation of 5 years. Please answer the followingquestions: a. Construct a 95% confidence interval estimate for themean of the consumers’ age. b. Suppose a sample of 85 was selected(with the same mean and the sample standard deviation). Construct a95% confidence interval for the mean of the consumers’ age.

[Hint: Please see Chap008 – Slides 24-29 for formula andexample. Please also see page 343-349 in the textbook.]

4. Hypothesis Testing Annual per captial consumption of milk is21.6 gallons (Statistical Abstract of the United States: 2006).Being from the Midwest, you believe milk consumption is higherthere and wish to support your opinion. A sample of 16 individualsfrom the Midwestern town of Webster City showed a sample meanannual consumption of 24.1 gallons with a sample standard deviationof s=4.8. a. Develop a hypothesis test that can be used todetermine whether the mean annual consumption in Webster City ishigher than the national mean. b. At α=0.05, test for a significantdifference. What is your conclusion? Extra credit 5. A lathe is setto cut bars of steel into lengths of 9 centimeters. The lathe isconsidered to be in perfect adjustment if the average length of thebars it cuts is 9 centimeters. A sample of 100 bars is selectedrandomly and measured. It is determined that the average length ofthe bars in the sample is 9.085 centimeters. Suppose the populationstandard deviation is 0.335 centimeters. a. Formulate thehypotheses to determine whether or not the lathe is in perfectadjustment. b. Compute the test statistic. c. Using the p-valueapproach, what is your conclusion? Let α = .05.