36. A random sample of 100 cereal boxes is selected and the frequency of occurrence is counted for each of four game cards contained in the boxes. The table lists the actual and expected frequen- cies of occurrence for each of the cards. Which of the following are valid conclusions? A B C D Card Actual Frequency 25 40 3 32 Expected Frequency 30 50 2 18 I. When a chi-square test is performed on the data, the test statistic equals 14.22. II. The degrees of freedom for this chi-square test are 3. III. For this chi-square test, these data are significant. (A) I (B) I and II (C) I, II, and III (D) I and III (E) A chi-square test cannot be performed. 37. Part of a printout of a computer regression analysis of the effect of a change in a manufac- turing process is shown. Output-A represents the output of stations before the change and Output-B represents the output of the stations after the change. Predictor Constant Output-A Coef StDev 81.29 88.30 0.92 0.82728 0.05364 15.42 P T 0.366 0.000 S = 314.6 R-Sq = 90.8% R-Sq(adj) = 90.5% Which of the following is the regression equation? = (A) Output-B= 81.29+ .82728(Output-A) (B) Output-A 81.29+ 82728(Output-B) (C) Output-B= .82728 + 81.29(Output-A) (D) Output-A = .82728 + 81.29(Output-B) (E) Output-B = .82728 + .05364(Output-A) 38. A light bulb manufacturer claims that its bulbs have a mean life of 139.5 hours with a standard deviation of 14.5 hours. You select a simple ran- dom sample to test this claim. Your sample of 10 bulbs has a mean life of 137.0 hours with a standard deviation of 12.5 hours. Which of the following would be the most appropriate test for establishing that the manufacturer's claim about the mean is high?(Assume that the distri- bution of light bulb lifetimes is normal.) (A) z-test for means (B) t-test for means (C) chi-square test (D) z-test for proportions (E) None of these tests would be appropriate. 39. A newspaper publishes a claim that 80% of stu- dents from its city's high schools go on to post- secondary education. A watch-dog group decides to test this hypothesis at the 5% level of confidence. Which of the following is not an appropriate interpretation of the 5% level of significance? (A) 5% is the probability of a Type I error. (B) 5% is the probability of rejecting the hypothesis that p-.80 when the hypothe- sis is true. (C) 5% is the probability of accepting the hypothesis that p = .80 when the hypothe- sis is false. (D) 5% is the criteria for judging whether the sample statistic is sufficiently extreme to cast doubt on the newspaper's claim. (E) All of these are appropriate interpretations of the 5%. 40. A two-tailed hypothesis (a = .05) of a popula- tion mean has a P-value of .072. Which of the following conclusions is valid? (A) The null hypothesis should be accepted. (B) The null hypothesis should be rejected. (C) A one-tailed test of the null hypothesis using the same sample will be significant. (D) The P-value of .072 indicates the probabil- ity that the null hypothesis is false. (E) The probability of seeing a statistic as extreme if the null hypothesis is true is .072