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

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 The data are analyzed by a standard program package SAS. The relevant output is shown here: a. What is the research hypothesis? b. What are the values of the t and t⬘ statistics? Why are they equal for this data set? c. What are the p-values for t and t⬘ statistics? Why are they different? d. Are the conclusions concerning the research hypothesis the same for the two tests if we use a ⫽ .05? e. Which test, t or t⬘, is more appropriate for this data set? Engin. 6.60 An industrial concern has experimented with several different mixtures of the four components—magnesium, sodium nitrate, strontium nitrate, and a binder—that comprise a rocket propellant. The company has found that two mixtures in particular give higher flare- illumination values than the others. Mixture 1 consists of a blend composed of the proportions .40, .10, .42, and .08, respectively, for the four components of the mixture; mixture 2 consists of a blend using the proportions .60, .27, .10, and .05. Twenty different blends 10 of each mixture are prepared and tested to obtain the flare-illumination values. These data appear here in units of 1,000 candles. Mixture 1 185 192 201 215 170 190 175 172 198 202 Mixture 2 221 210 215 202 204 196 225 230 214 217 a. Plot the sample data. Which tests could be used to compare the mean illumination values for the two mixtures? b. Give the level of significance of the test and interpret your findings. 6.61 Refer to Exercise 6.60. Instead of conducting a statistical test, use the sample data to answer the question, What is the difference in mean flare illumination for the two mixtures?

6.62 Refer to Exercise 6.60. Suppose we wish to test the research hypothesis that m

1 ⬍ m 2 for the two mixtures. Assume that the population distributions are normally distributed with a common s ⫽ 12. Determine the sample size required to obtain a test having a ⫽ .05 and bm d ⬍ .10 when m 2 ⫺ m 1 ⱖ 15. 6.63 Refer to the epilepsy study data from Chapter 3. An analysis of the data produced the fol- lowing computer output. The measured variable is the number of seizures after 8 weeks in the study for patients on the placebo and for those treated with the drug progabide. Two-Sample T-Test and Confidence Interval Two-sample T for Placebo vs Progabide N Mean StDev SE Mean Placebo 28 7.96 7.63 1.4 Progabide 31 6.7 11.3 2.0 95 CI for mu Placebo mu Progabide: 3.8, 6.3 T-Test mu Placebo mu Progabide vs : T 0.50 P 0.31 DF 57 Both use Pooled StDev 9.71 TEST PROCEDURE Variable: POTENCY SAMPLE N Mean Std Dev Std Error Variances T DF Prob T -------------------------------------------------- ---------------------------------- 1 10 10.37000000 0.32335052 0.10225241 Unequal 4.2368 16.6 0.0006 2 10 9.83000000 0.24060110 0.07608475 Equal 4.2368 18.0 0.0005 For HO: Variances are equal, F 1.81 DF 9,9 Prob F 0.3917