Q1. Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a population mean of 22,100 miles. A manufacturer of spark plugs claims that its plugs have an average life in excess of 22,100 miles. The fleet owner purchased 18 sets and found that the sample average life was 23,400 miles, the sample standard deviation was 1,500 miles and the calculated value of t = 3.677. Based on these findings, is there enough evidence to accept the manufacturer's claim at the 0.05 level. (Explain your answer)
Q2. The mean life of a battery used in a digital clock is 305 days. The lives of the batteries follow the normal distribution. The battery was recently modified to last longer. A sample of 20 of the modified batteries had a mean life of 311 days with a standard deviation of 12 days. You have been asked to test if the modifications have increased the mean life of the batteries at the .05 significance level.
a) State the null & alternative hypothesis:
b) Compute the test statistic and indicate your decision regarding the null hypothesis? Hint: First determine your decision rule.
Q3. As a region sales manager you are interested in testing if there is a difference in sales close rates between two of your sales regions. In the west region you contacted 50 sales people and found that they closed a sale at a rate of 40% of the time. The East region had a higher close rate at 50% based on a sample of 80. In the space below write the formula for the test statistic used to evaluate the difference. Second complete (fill in the values) the formula using the information above. Do not calculate the final value of the test statistic.