# Exam 1 review

## Statistics 350 with Gunderson at University of Michigan - Ann Arbor *

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Stat 350 F08 Exam 1 Review page 1 of 6 OVERVIEW: Stat 350 Exam 1 Review Sunday, October 12,7-8:30 pm in MLB AUD 3 Please print out, try out, and bring these questions with your Qwizdom clicker to the review session if you attend! This review will be captured and posted by Monday pm. Solutions will be posted by Sunday 10 pm on Ctools. DATA Yes 18 1. 2 No 21 1. 1 No 20 1. 3 … … … Stat 350 F08 Exam 1 Review page 2 of 6 Ho w i s DA TA gat he red? Rand om Variable s Stat 350 F08 Exam 1 Review page 3 of 6 1. Suppose that 2000 customers shopped at a mall and their results regarding their age category and gift-receiving preference are summarized below. Use these results to answer the following questions regarding this population of 2000 mall shoppers. Would prefer an electronic gift Would not prefer an electronic gift Total Under 30 600 200 800 30 or over 900 300 1200 Total 1500 500 2000 a. What is the probability that a randomly selected mall shopper would prefer an electronic gift? b. Suppose a mall shopper is under 30 years of age, what is the probability that they would prefer an electronic gift? c. Based on these results, are age category and gift-receiving preference independent for this population? Give clear support for your answer. 2. College Student Piracy: A recent article described how the Motion Picture Association of America (MPAA) overestimated the amount of money the industry lost to piracy by college students. You have been asked to help design a study to estimate the proportion of all current UM students that have illegally shared files. a. If a 99% conservative confidence level is to be used, what minimum sample size would be needed to estimate the UM rate to within 4%? Show all work. b. Suppose another university has conducted a similar study and their resulting 99% conservative confidence interval was found to be (0.10, 0.20). i. What proportion of the students sampled stated they had illegally shared files? ii. The two researchers have each written up an interpretation of the level of confidence for including in their report. Review each interpretation and circle your answer. Researcher 1: We would expect the population proportion of all such college students who have illegally shared files to be between 0.10 and 0.20 at least 99% of the time, if this procedure were repeated many times, Researcher 2: If we repeated this procedure many times, we would expect (at least) 99% of the intervals to contain the population proportion of all such college students who have illegally shared files. Select one: Both interpretations are correct. Only Researcher 1’s interpretation is correct. Only Researcher 2’s interpretation is correct. Neither interpretation is correct. Stat 350 F08 Exam 1 Review page 4 of 6 3. The Books-for-Cheap (BFC) on-line company prides itself in having its orders delivered on time. They would like to claim that more than 90% of its orders are delivered on time. They ask a consulting group to conduct a study to test the following hypotheses. H0: p = 0.90 versus Ha: p > 0.90 a. Complete the statement of hypotheses by identifying the parameter of interest and defining it in the context of this problem. where ______ is defined as … __________________________________________________ _________________________________________________________________________ b. From a random sample of 20 orders, 19 were delivered on time. Give the value of the appropriate test statistic and corresponding p-value for the test. Show all work. Test Statistic Value: ___________________ p-value: ___________________________ c. State your decision using a significance level of 5%, your reason for making your decision, and the corresponding conclusion. Your conclusion should be in the context of the problem. Decision: (circle one) Reject H0 Fail to reject H0 Explain why: Conclusion: d. Your decision in part (c) could be wrong. What type of error could have been made? ____________ Stat 350 F08 Exam 1 Review page 5 of 6 4. Vitamin C and the Common Cold: Wisconsin’s Department of Public Health has extensively studied winter colds. With the daily use of vitamin C, the probability a Wisconsin resident survives a winter season without a cold is 0.63. As part of a study, 100 Wisconsin residents who take vitamin C daily will be chosen at random. Let X be the number in the sample that survive the winter season without a cold. a. How many residents in the sample would be expected to survive the winter season without a cold? b. Suppose 52 of the selected residents survived the winter season without a cold. How many standard deviations does this observed value of 52 fall below the mean? c. If the true survival rate is indeed 63%, how likely would it be to observe only 52 or fewer of the sampled vitamin C using residents survive the winter season without a cold? d. If a researcher were using the study results to test the theory that the true survival rate is less than the stated 63%, what is the statistical name for the probability found in part (c)? 5. Faculty Salaries: During the 2006-2007 academic year, Assistant Professors in Psychology earned on average of $50.7 (nearest thousand) per year with a standard deviation of $2.9 (nearest thousand). Salaries for this population can be modeled as approximately normal. a. What proportion of Assistant Professors in Psychology earned at least $45,000 for the 2006-2007 year? Show all work, including a sketch of what value you are asked to find. b. To the nearest $1000, about 25% of the Assistant Professors in Psychology earned at least how much? Show all work, including a sketch of what value you are asked to find. Stat 350 F08 Exam 1 Review page 6 of 6 6. Think women talk more? Study says no. In a study, researchers placed microphones on a sample of college students and calculated how many words they used in the course of a day. The average number of words used daily for the women in the study was 16,215, while the average for the men was 15,669. The difference: Just 546 words. a. Which of the following pertain to the value of 16,215? Circle all that apply. statistic sample mean parameter x population mean b. Suppose the standard deviation for the number of words used for the women in the study was 3,120. Clearly interpret this standard deviation in terms of an average distance. c. Side by side boxplots are provided. Fill in the blank: The least talkative male used about _______ words True or False? The boxplot of the number of words used for the women college students confirms the distribution is symmetric. Circle one: T F Explain: 7. A small manufacturer produces cups used by a coffee store chain for serving coffee. At a recent strategy meeting some changes to the current production process were proposed that might put the workers on an initial learning curve, but it would involve minor equipment changes at a very low cost, and could lead to a higher mean production level. It was decided to set up this new production process and run an experiment. The data for a 60-day production run under this new process have just come in (number of cups produced daily). An employee at the company has entered the data into SPSS and needs your assistance as to what to do next. Consider the following possible statistical summaries: 1. Compute the sample mean production level for the 60 days 2. Make a time plot of the production levels 3. Make a histogram of the production levels These summaries should be performed in a particular order. What is that order (which summary should be examined first, which should come next, and then which should be last)? anilg Questions for exam 1

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