Confidence interval estimates

1. One operation of a mill is to cut pieces of steel into parts that are used in the frame for front seats in an automobile. The steel is cut with a diamond saw, and the resulting parts must be cut to be within +/- 0.005 inch of the length specified by the automobile company. The measurement reported from a sample of 100 steel parts (Stored in Steel) is the difference, in inches, between the actual length of the steel part, as measured by a laser measurement device, and the specified length of the steel part. For example, the first observation, -0.002 represents a steel part that is 0.002 inch shorter than the specified length.

Please see the attached Excel document for the data.

a. Construct a 95% confidence interval estimate for the population mean difference between the actual length of the steel part and the specified length of the steel part.
b. What assumption must you make about the population distribution in order to construct the confidence interval estimate in (a)?
c. Do you think that the assumption needed in order to construct the confidence interval estimate in (a) is valid? Explain.

2. Although many people think they can put a meal on the table in a short period of time, an article reported that they end of spending about 40 minutes doing so. Suppose another study is conducted to test the validity of this statement. A sample of 25 people is selected, and the length of time to prepare and cook dinner (In minutes) is recorded with the following results in (Dinner):

44.0 51.9 49.7 40.0 55.5 33.0 43.4 41.3 45.2 40.7 41.1 49.1 30.9
45.2 55.3 52.1 55.1 38.8 43.1 39.2 58.6 49.8 43.2 47.9 46.6

a. Is there evidence that the population time to prepare and cook dinner is different from 40 minutes? Use the p-value approach and a level of significance of 0.05.
b. What assumption about the population distribution is needed in order to conduct the t test in (a)?
c. Make a list of the various ways you could evaluate the assumption noted in (b).
d. Evaluate the assumption in (b) and determine whether the t test in (a) is valid.