Statistics: t-value, z-value and null hypothesis

1. A random sample of size 81 is taken from a large population, measuring the time it takes to complete a driver's license examination. The sample mean was found to be 43 minutes, and the sample standard deviation 5.71 minutes. Construct a 95% confidence interval around the sample mean. Be sure to show whether you use the t- or z- value, and what value you use. Even though you are normally 'allowed' to use an approximate value of 't' or 'z' for this percent confidence, use the exact value appropriate for these circumstances. Interpret the confidence interval in a single sentence. In another sentence, state why you used either the 't' or the 'z'.

2. According to the Bureau of Labor Statistics, the average weekly earnings of a production worker in 2009 were $519.35. You are interested to know if wages, on average, have gone up since that time. To test this, you sample 64 production workers, and determine that their average salary is $525.00, with a sample standard deviation of $33.90. Use a 0.05 level of significance.

a. State the null and alternative hypothesis that best tests the hypothesis of interest. Be sure to pay attention to whether this should be a 1-tailed or a 2-tailed test.

b. Carry out this test, and state whether you reject or fail to reject the null hypothesis. In computing the test statistic, be sure to indicate whether you are using 't' or 'z'. Use the precise critical value of the 't' or 'z', not an approximation.