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Name___________________________ AP Stats Ch.10 Test 2021 CORONA An experiment was conducted to assess the efficacy of spraying oats with malathion (at 0.25 lb/acre) to control the cereal leaf beetle. A sample of 10 farms was selected at random from southwest Manitoba. Each farm was assigned at random to either the control group (no spray) or the treatment group (spray). At the conclusion of the experiment, a plot on each farm was selected, the number of larvae per stem was measured, and a one- tailed test of significance was performed to determine if malathion reduced the number of beetles. Here are two possible outputs from MINITAB, only one of which is correct (some output hidden): 1) Which of the following is the appropriate test statistic and a possible P-value? (a) 1.896, 0.065 (b) 1.896, 0.131 (c) 1.896, 0.013 (d) 1.887, 0.059 (e) 1.887, 0.118 2) In which one of the following cases would a Type I error occur? (a) We do not conclude malathion is effective when in fact it was effective. (b) We conclude malathion is effective when in fact it is ineffective. (c) We conclude malathion is effective when in fact it is effective. (d) We do not conclude malathion is effective when in fact it is ineffective. (e) We conclude malathion is neither ineffective nor effective.

3) The following are percents of fat found in 6 samples of each of two brands of Cheese: A 5.7 4.5 6.2 6.3 6.3 7.3 B 6.3 5.7 5.9 6.4 6.4 5.1 Which of the following procedures is appropriate to test the hypothesis of equal average fat content in the two types of cheese? (a) Paired t test with 5 df. (b) Two-sample t test with 4 df. (c) Paired t test with 4 df. (d) Two-sample t test with 5 df. (e) Two-proportion z test. 4) Which of the following describes a situation in which it is safe to employ t-procedures (a) n1 =10, n2 = 40; both samples are moderately skewed. (b) n1 =10, n2 = 8; sample 1 is approximately normal, while sample 2 is skewed right. (c) n1 =6, n2 = 6; both samples are approximately normal. (d) n1 =35, n2 = 40; both samples are approximately normal, sample 2 has two outliers. (e) It is safe to use t-procedures in more than one of the situations above. 5) A consumer group has determined that the distribution of life spans for gas ranges (stoves) has a mean of 15.0 years and a standard deviation of 4.2 years. The distribution of life spans for electric ranges has a mean of 13.4 years and a standard deviation of 3.7 years. Both distributions are moderately skewed to the right. Suppose we take a simple random sample of 35 gas ranges and a second SRS of 40 electric ranges. Which of the following best describes the sampling distribution of G E x x − , the difference in mean life span of gas ranges and electric ranges? A) Mean = 1.6 years, standard deviation = 7.9 years, shape: moderately right-skewed. B) Mean = 1.6 years, standard deviation = 0.92 years, shape: approximately Normal. C) Mean = 1.6 years, standard deviation = 0.92 years, shape: moderately right skewed. D) Mean = 1.6 years, standard deviation = 0.40 years, shape: approximately Normal. E) Mean = 1.6 years, standard deviation = 0.40 years, shape: moderately right skewed.

For questions 6 and 7: In a large Midwestern university (with the class of entering freshmen being on the order of 6000 or more students), an SRS of 100 entering freshmen in 1993 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 1995. In 1997, an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. Let p1 be the proportion of all entering freshmen in 1993 who graduated in the bottom third of their high school class, and let p2 be the proportion of all entering freshmen in 1997 who graduated in the bottom third of their high school class. 6) Which of the following represents 99% confidence interval for p1 – p2? 7) Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 1997 has been reduced as a result of the tougher admission standards adopted in 1995, compared to the proportion in 1993? To determine this, you test the hypotheses H0: p1 = p2, Ha: p1 > p2 at the  = 0.05 level. You calculate a test statistic of 1.980. Which of the following is the appropriate P- value and conclusion for your test? A) P-value = 0.047; fail to reject H0; we do not have evidence that the proportion who graduated in the bottom third of their class has been reduced. B) P-value = 0.047; accept Ha; there is evidence that the proportion who graduated in the bottom third of their class has been reduced. C) P-value = 0.024; fail to reject H0; we do not have evidence that the proportion who graduated in the bottom third of their class has been reduced. D) P-value = 0.024; reject H0; we have evidence that the proportion who graduated in the bottom third of their class has been reduced. E) P-value = 0.024; fail to reject H0; we have evidence that the proportion who graduated in the bottom third of their class has not changed.

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