Suggest a procedure by which we could be ensured that the experiment-wide Type I

Med. 6.54 To assess whether degreed nurses received a more comprehensive training than registered nurses, a study was designed to compare the two groups. The state nursing licensing board ran- domly selected 50 nurses from each group for evaluation. They were given the state licensing board examination and their scores are summarized in the following tables and graphs.

a. Can the licensing board conclude that the mean score of nurses who receive a BS in

nursing is higher than the mean score of registered nurses? Use a ⫽ .05. b. Report the approximated p-value for your test. c. Estimate the size of the difference in the mean scores of the two groups of nurses using a 95 confidence interval.

d. The mean test scores are considered to have a meaningful difference only if they differ

by more than 40 points. Is the observed difference in the mean scores a meaningful one? Pol. Sci. 6.55 All persons running for public office must report the amount of money spent during their campaign. Political scientists have contended that female candidates generally find it difficult to raise money and therefore spend less in their campaign than male candidates. Suppose the accompanying data represent the campaign expenditures of a randomly selected group of male and female candidates for the state legislature. Do the data support the claim that female candi- dates generally spend less in their campaigns for public office than male candidates? Campaign Expenditures in thousands of dollars Candidate 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

19 20

Female 169

206 257

294 252 283 240 207 230 183 298 269 256 277 300 126 318 184 252 305 Male 289 334 278 268 336 438 388 388 394 394 425 386 356 342 305 365 355 312 209 458

a. State the null and alternative hypotheses in

i. Plain English ii. Statistical terms or symbols

b. Estimate the size of the difference in campaign expenditures for female and male

candidates. c. Is the difference statistically significant at the .05 level? d. Is the difference of practical significance? 6.56 Refer to Exercise 6.55. What conditions must be satisfied in order to use the t procedures to analyze the data? Use the accompanying summary data and plot to determine whether these conditions have been satisfied for the data in Exercise 6.55. Two-Sample T-Test and Confidence Interval Two-sample T for Degreed vs RN N Mean StDev SE Mean Degreed 50 399.9 17.2 2.4 RN 50 354.7 30.9 4.4 95 CI for mu Degreed - mu RN: 35.3, 55.2 T-Test mu Degreed mu RN vs : T 9.04 P 0.0000 DF 76 450 400 350 300 Degreed nurses Registered nurses Examination scores Boxplots of degreed and registered nurses means are indicated by solid circles 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