Hypothesis Testing of Unit Production

1. An industrial engineer at Lyons Products would like to determine whether there are more units produced on the afternoon shift than on the morning shift. A sample of 50 morning-shift workers showed that the mean number of units produced was 345, with a standard deviation of 21. A sample of 60 afternoon-shift workers showed the mean number of units produced was 351, with a standard deviation of 28 units. At the .05 significance level, is the mean number of units produced on the afternoon-shift larger? (state the hypothesis, critical value(s), decision rule, test statistic,decision, and conclusion)

2. A statistics professor would like to determine whether students in the class showed improved performance on the final exam as compared to the midterm examination. A random sample of 7 students selected from a large class revealed the following scores: midterm 70, 62, 57, 68, 89, 63, 82 and on the final 80, 79, 87, 88, 85, 79, 91. Is there evidence of an improvement on the final examination, at the 1% significance level? (state the hypothesis, critical value(s), decision rule, test statistic,decision, and conclusion)

3. There are two car dealerships in a particular area. The mean monthly sales at the two dealerships are about the same. However, one of the dealerships (dealership A) is boasting to corporate headquarters that his dealershipâ??s monthly sales are more consistent. An industry analyst reviews the last seven months at dealership A and finds the standard deviation of the seven monthly sales to be 14.79. He reviews the last eight months at dealership B and finds the standard deviation of the eight monthly sales to be 22.95. Using the .01 significance level does the analyst find evidence that the boast of dealership A is correct? (state the hypothesis, critical value(s), decision rule, test statistic, decision, and conclusion)