4. Test identification: Suppose you were asked to analyze each of the situations described below. (NOTE: Do not do these problems!) For each, indicate which procedure you would use (pick the appropriate number from the list), the test statistic (z or t), and, if t, the number of degrees of freedom. A procedure may be used more than once.
1. proportion - 1 sample
2. difference of proportions, 2 samples
3. mean - 1 sample
4. difference of means - independent samples
5. mean of differences - matched pairs
a. A union organization would like to represent the employees at the local market. A sample of the employees revealed 74 of 120 were in favor of the union. Does the union have the required 3 to 2 majority?
b. An oral surgeon is interested in estimating how long it takes to extract all four wisdom teeth. The doctor records the times for 24 randomly chosen surgeries. Estimate the time it takes to perform the surgery with a 95% confidence interval.
c. A microwave manufacturing company receives large shipments of thermal shields from two suppliers. A sample from each supplier's shipment is selected and tested for the rate of defects. The microwave manufacturing company's contract with each supplier states the shipment with the smallest rate of defect will be accepted. Do the shipments' defect rates vary from each other?
d. The owner of a construction company would like to know if his current work teams can build room additions quicker than the time allotted for by the contract. A random sample of 15 room additions completed recently revealed an average completion time of 0.32 days faster than contracted. Is this strong evidence that the teams can complete room additions in less than the contract times?
e. A farmer would like to know if a new fertilizer increases his crop yield. In an effort to decide this, the farmer recorded the yield for 10 different fields prior to adding fertilizer and after adding the fertilizer. The farmer assumes the crop yields are approximately normal. Does the fertilizer work as advertised?
f. In a study to determine whether there is a difference between the average jail time convicted bank robbers and car thieves are sentenced to, the law students randomly selected 20 cases of each type that resulted in jail sentences during the previous year. A 90% confidence interval was created from the results.