AP Statistics Chapter 10 Test: Efficacy of Malathion Explained

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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8) An SRS of size 100 is taken from Population A with proportion 0.8 of successes. An independent SRS of size 400 is taken from Population B with proportion 0.5 of successes. The sampling distribution for the difference (Population A – Population B) in sample proportions has what mean and standard deviation? (a) mean = 0.3; standard deviation = 0.047 (b) mean = 0.3; standard deviation = 0.40 (c) mean = 0.3; standard deviation = 0.0747 (d) mean = 0.3; standard deviation = 0.0022 (e) mean = 0.3; standard deviation = 0.0002 9) A political candidate testing the effectiveness of a new advertisement takes a simple random sample of 300 voters before the ad goes on air and another sample of 250 voters afterwards. 158 of the 300 voters in the “before” sample say they support his candidacy, and 140 voters in the “after” sample say they support him. If A p = proportion approving his candidacy in the after sample and B p = proportion approving his candidacy in the before sample, which of the following is the correct test statistic for : 0 A B Ho P P − =

10) A random sample of 30 words from Jane Austen’s Pride and Prejudice had a mean length of 4.08 letters with a standard deviation of 2.40. A random sample of 30 words from Henry James’s What Maisie Knew had a mean length of 3.85 letters with a standard deviation of 2.26. Which of the following is a correct expression for the 99% confidence interval for the difference in mean word length for these two novels? 2.756 should read 2.576. Sorry. 11) A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. Construct a 95% confidence interval for the mean difference between the before and after scores 12) Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2, Use the given sample sizes and numbers of successes to find the pooled estimate ˆ c p . Round your answer to the nearest thousandth. No work needed. n1 = 100 x1 = 42 n2 = 100 x2 = 45 13) Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2, Use the given sample sizes and numbers of successes to find the P-value for the hypothesis test. No work needed. n1 = 50 x1 = 8 n2 = 50 x2 = 9

14) Independent samples from two different populations yield the following data. 1 x = 958, 2 x = 157 s1 = 77, s2 = 88. The sample size is 478 for both samples. Find the 90% confidence inter val for μ1 - μ2. No work needed. 15) Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis We wish to compare the means of two populations using paired observations. Suppose that d = 3.125, Sd = 2.911, and n = 8, and that you wish to test the following hypothesis at the 10% level of significance: H0: μd = 0 against H1: μd > 0 What decision rule would you use? A) Reject H0 if test statistic is less than 1.415. B) Reject H0 if test statistic is greater than -1.415. C) Reject H0 if test statistic is greater than -1.415 and less than 1.415. D) Reject H0 if test statistic is greater than 1.415. 16) The mean score on a science assessment for 49 SRS male high school students was 149 with a standard deviation of 35. The mean score on the same test for 50 SRS female high school students was 145 with a standard deviation of 33. a) Find the numeric value of the standard error. Nearest 1000 th . b) Test the claim that the mean score on the science assessment for the male high school students was higher than for the female high school students? Alpha = 0.05. Assume all conditions

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Name___________________________ AP Stats Ch.10 Test 2021 CORONA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

AP Ch.10 Two Pops Test 2021

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