5. Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean 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 1,412 miles. To decide if the sample data support the company records that the spark plugs average 22,100 miles, state your decision in terms of the null hypothesis. Use a 0.05 level of significance.
6. A machine cuts steel to length for nails. The mean length of a nail is 43 millimeters. There is concern that the settings of the machine producing the nails have changed. To test the claim, twelve nails (n = 12) were sampled. The mean of the sample is 41.5 and the standard deviation is 1.784. To test the claim at the 0.02 significance level, what is the critical value?