State the null and alternative hypotheses in

Two-Sample T-Test and Confidence Interval Two-sample T for Female vs Male N Mean StDev SE Mean Female 20 245.4 52.1 12 Male 20 350.9 61.9 14 95 CI for mu Female - mu Male: 142, 69 T-Test mu Female mu Male vs not : T 5.83 P 0.0000 DF 38 Both use Pooled StDev 57.2 Boxplots of female and male candidates means are indicated by solid circles Female candidates Male candidates 500 400 300 200 100 Campaign expenditures in thousands of dollars Env. 6.57 After strip mining for coal, the mining company is required to restore the land to its con- dition prior to mining. One of many factors that is considered is the pH of the soil, which is an im- portant factor in determining what types of plants will survive in a given location. The area was divided into grids before the mining took place. Fifteen grids were randomly selected and the soil pH was measured before mining. When the mining was completed, the land was restored and an- other set of pH readings were taken on the same 15 grids; see the accompanying table. Location 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Before 10.02 10.16 9.96 10.01 9.87 10.05 10.07 10.08 10.05 10.04 10.09 10.09 9.92 10.05 10.13 After 10.21 10.16 10.11 10.10 10.07 10.13 10.08 10.30 10.17 10.10 10.06 10.37 10.24 10.19 10.13

a. What is the level of significance of the test for a change in mean pH after reclamation

of the land? b. What is the research hypothesis that the land office was testing? c. Estimate the change in mean soil pH after strip mining using a 99 confidence interval.

d. The land office assessed a fine on the mining company because the t test indicated a

significant difference in mean pH after the reclaimation of the land. Do you think their findings are supported by the data? Justify your answer using the results from parts a and c. 6.58 Refer to Exercise 6.57. Based on the land office’s decision in the test of hypotheses, could they have made select one of the following a. A Type I error? b. A Type II error? c. Both a Type I and a Type II error? d. Neither a Type I nor a Type II error? Med. 6.59 Company officials are concerned about the length of time a particular drug retains its po- tency. A random sample sample 1 of 10 bottles of the product is drawn from current production and analyzed for potency. A second sample sample 2 is obtained, stored for 1 year, and then analyzed. The readings obtained are as follows: Sample 1 10.2 10.5 10.3 10.8 9.8 10.6 10.7 10.2 10.0 10.6 Sample 2 9.8 9.6 10.1 10.2 10.1 9.7 9.5 9.6 9.8 9.9