Cover Page Homework #9 1. The number of observations needed to satisfy the court stipulations is: round-up! 2. Problem 14.24 (a) z = Problem 14.28 (a) The margin of error for this interval will be: (b) 99% confidence interval: Problem 14.30 (a) Average weight: Problem 14.34 (a) 99% CI for µ: (b) Answer: Problem 14.38 (a) Correct? (b) Explain your answer: 3. (a) Blank #1: (b) Blank #2: 4. (a) The average degradation in performance due to marijuana is: (b) Give-or-take: 1
(c) 95% CI: (d) Express the 95% CI in laymen terms: Is there evidence that marijuana affects IQ test-taking adversely? Yes or No: (e) Explain briefly: (f) Is the observed difference (g) Is there evidence that ordingary cigareet smoking affects large in practical terms? performance? Attach your homework packet and your answers for the remaining problems. 2
MODESTO JUNIOR COLLEGE Department of Mathematics MATH 134 Fall 2011 Homework #9 Due by 5pm on Tuesday, November 8 th. In this homework we continue our exploration of Probability and Statistical Models, sample size determination, statistical and practical significance. As usual, show sufficient work in order to receive full credit for an answer. Express answers to research questions using full sentences. NOTE: It is not required to set up the Probability or Statistical Models, unless otherwise stated. 1. (business) As we saw in the C&O freight study in class, it has become common in recent years for evidence based on sampling to be used informally by companies, or even formally presented in court, to figure out accounts receivable or settle disputes. For instance, when sample evidence is submitted to a court to justify deductions from taxable profits for expenses incurred in a long series of transactions, it is typically stipulated by the court that the sample estimate of the average of the average expenses per transaction be correct to within some tolerance like $500 with at least 95% probability. From past experience a given firm will know how much variability the distribution of expenses per transaction has, for example a standard deviation of $1800. The company you work for decides tentatively to take a simple random sample of 40 transactions to estimate the overall average expenses per transaction. Create a statistical model, describe the population, sample and imaginary data sets. Identify the variable of interest. Draw the shape of the population, sample and imaginary data set histograms. Show that the chance your sample mean will be correct to within the court s stipulation is only about 92%. How many observations would you actually need to satisfy the court? Explain briefly. 2. Problems from Moore s text: 14.21, 14.24, 14.27, 14.28 - and find the 99% confidence interval for the true weight of this specimen, 14.30, 14.34, 14.35, 14.37, 14.38 3. Here is an explanation from the Associated Press concerning one of its opinion polls. Fill-in the blanks: For a poll of 1,600 adults, the variation due to sampling error is no more than three percentage points either way. The error margin is said to be valid at the 95 percent confidence level. This means that, if the same questions were repeated in 20 polls, the results of about surveys would be within three percentage points of the.
4. (psychology) About 35 years ago the issue of whether marijuana cases degradation of intellectual performance was a hot topic in psychology. Several investigators writing in Science in 1968 were interested in the effect of marijuana on the performance on IQ tests of subjects who had no previous experience with the drug. They ran a randomized experiment on 30 volunteers who were ordinary cigarette smokers, and the design went like this. Each person took an IQ test, smoked a cigarette, took another IQ test, and then came back the next day and did it again. An ordinary cigarette was smoked on one day and a marijuana cigarette the other, with the order randomized for each subject. The table at right gives the change in performance (after IQ score - before IQ score) for each subject under the two treatment conditions. Estimate the average degradation in performance caused by marijuana, attach a standard error to this estimate, and build a 95% confidence interval for the typical degradation. Is there evidence that marijuana affects IQ test-taking adversely? Explain briefly. Comment on whether the observed difference is large in practical terms (the average IQ in the population is about 100 with an SD of about 15). CIGARETTE difference Subject Ordinary Marijuana (M-O) 1-4 -22-18 2-2 -17-15 3 5 11 6 4 8 4-4 5 1-6 -7 6 1 2 1 7 10 5-5 8 6 8 2 9-4 -3 1 10 2 5 3 11-3 -14-11 12 7 7 0 13 1-20 -21 14-1 -4-3 15-6 -7-1 16 2 1-1 17-3 -17-14 18 6-3 -9 19 13-3 -16 20-1 9 10 21-4 -26-22 22-3 5 8 23 10-17 -27 24-3 -7-4 25 3-3 -6 26 4-7 -11 27-3 -9-6 28 2-6 -8 29-1 1 2 30-1 3 4 mean 1.4-4.3-5.7 SD 4.9 9.9 9.2 Is there evidence that ordinary cigarette smoking enhances or degrades performance? Make any calculations you find helpful to support your argument. In addition to changing the mean, is there evidence that marijuana changes anything else about people s IQ test-taking? Explain briefly, and summarize your overall conclusions. 5. Successful hotel managers must have personality characteristics often thought of as masculine (such as forceful.) The Bem Sex-Role Inventory (BSRI) is a personality test that gives separate ratings for female and male stereotypes, both on a scale of 1 to 7. You plan to take a sample of male general managers of three-star and four-star hotels and would be satisfied to estimate the mean BSRI score for the population of all male 3-star and 4-star hotel managers within ±0.2 with 99% confidence. How large 4
of an SRS of hotel managers do you need? Assume that the SD of scores in the sample of hotel managers is the same as the population SD of 0.78. 6. A market researcher chooses at random from women entering a large suburban shopping mall. One outcome of the study is a 95% confidence interval for the mean of the highest price you would pay for a pair of casual shoes. (a.) Explain why this confidence interval does not give useful information about the population of all women. (b.) Explain why it may be useful information about the population of women who shop at large suburban malls. 7. The National AIDS Behavioral Surveys found that 170 individuals in its random sample of 2673 adult heterosexuals said they had multiple sexual partners in the past year. That s 6.36% of the sample. Why is this estimate likely to be biased? Does the margin of error of a 95% confidence interval for the proportion of all adults with multiple partners allow for this bias? 5