14. 12. To determine whether training in a series of workshops on creative thinking increases IQ scores, a total of 70 students are randomly divided into treatment and control groups of 35 each. After two months of training, the sample mean IQ (X1) for the treatment group equals 110, and the sample mean IQ (X2) for the control group equals 108. The estimated standard error equals 1.80.

(a). Using t, test the null hypothesis at the .01 level of significance.

(b). If appropriate (because the null hypothesis has been rejected), estimate the standardized effect size, construct a 99 percent confidence interval for the true population mean difference, and interpret these estimates.

15.9. A manufacturer of a gas additive claims that it improves gas mileage. A random sample of 30 drivers tests this claim by determining their gas mileage for a full tank of gas that contains the additive (X1) and for a full tank of gas that does not contain the additive (X2). The sample mean difference, D, equals 2.12 miles (in favor of the additive), and the estimated standard error equals 1.50 miles.

(a). Using t, test the null hypothesis at .05 level of significance

(b). Specify the p-value for this result

(c). Are there any special precautions that should be taken with the present experimental design?