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Ecn. 220 Fall 2002 Todd Easton Final Exam Before beginning the exam, please read the following pledge and sign it. Return this sheet with your exam answers. I promise that I will not send or receive email, or surf the Web, during this class period. I promise that I won’t look at other students’ monitors or exams. I promise that the only outside materials I relied upon were my three 3 x 5” cards. I promise that the work I turn in is mine alone. __________ Please answer each of the following questions. Show all your work (if you use Excel, type or copy each formula). Unless a specific method of answering a question is specified, feel free to select a method of your own choosing (e.g. paper and pencil or Excel). Please write answers only on the front of each sheet you use and please put your name on the back of each sheet. I’d like to grade each exam without knowing the identity of the author. If a question is about a sampling situation, assume the population size is very large, compared to the sample, unless the question says otherwise. 1) Of employed US adults age 25 or older, 90.5% have completed high school, while 29.7% have completed college. Suppose one is selecting from this population at random. Also, suppose that everyone who completed college also completed high school. Given that you select that someone has completed high school, what is the chance they also completed college? 2) You recently initiated a new marketing campaign. The goal of the campaign is for more than 25% of supermarket shoppers to recognize your company’s brand. You just got back the results from a survey of 150 random shoppers: 28.2% recognized your brand name. a) Suppose you are clear that the burden of proof is on you to show that, at the 5% confidence level, the goal of the campaign has been reached. What is your null hypothesis? Please explain your choice. b) Perform the test of the hypothesis you selected in a). Present the result and explain it. Make the explanation clear enough that someone who never studied statistics could understand it. 3) A machine fills 12-ounce cans. It misfills a can 0.1% of the time. a) If a case of 24 cans is tested for proper filling, what is the probability that there is 1 incorrectly filled can? b) If a case of 24 cans is tested, what is the probability that there is 1 or more incorrectly filled can? 2 *************** For the fourth question on the exam, you have a choice. Please do only one of the following: 4A or 4B. 4A) Suppose you are responsible for product quality at a paper plant. You take random samples of output during each two-hour period. For one particular two-hour period, the sample mean was 4.015 thousandths of an inch for the 16 sheets you sampled. The sample standard deviation was .00675 thousandths of an inch. a) Explain the meaning of the sample standard deviation number. b) Calculate a 95% confidence interval for the population mean paper thickness. c) Would you need to make any assumptions to calculate this interval? Please explain. 4B) Below find two regressions. Please describe the difference between the scatters of points in the two diagrams. Please explain the difference in the strength of the two x-y relationships graphed. In your explanation of the strength difference, please comment both on the slope coefficient estimated and on the R2. Predicting y: Regression 1 y 300 250y = 3.9727x + 28.532 200 150 100 50 2 R = 0.6836 0 -50 0 10 20 30 40 50 60 50 60 x Predicting y: Regression 2 y' 300 250 200 150 100 50 y = 2.5287x - 25.812 0 -50 0 2 R = 0.891 10 20 30 x *************** 40 3 5) A student of mine, Piti Tantivirasut, was interested in tourism to Thailand. He used Excel to estimate the model given below. His dependent variable was the number of tourists arriving in Thailand in a particular quarter (Q1=January-March, Q2=April-June, Q3=July-September, Q4=October-December) during a fouryear period. He reasoned that: tourism was highest during the fourth quarter, when weather was particularly good, so he included in his model a dummy variables: Q4=1 if the arrivals are during the fourth quarter and otherwise =0. there was general rise in tourism to Thailand, so he included a variable that increased by one with each passing quarter (Time). Figure 1, Predicting Tourism in Thailand between 1997, Q1 to 2000, Q4 Regression Statistics Multiple R 0.899 R Square 0.808 Adjusted R Square 0.778 Standard Error 153206 Observations 16 ANOVA df Regression SS 2 MS 1.28015E+12 6.4E+11 Residual 13 3.05136E+11 2.35E+10 Total 15 1.58529E+12 Coefficients Standard Error Intercept Q4 Time 1612380 332893 47247 80845 90057 8459 t Stat 19.94 3.70 5.59 a) Explain the meaning of the coefficients on the two variables Q4 and Time, from the results presented in Figure 2. b) Please use the t-statistic for Q4 to test the the null hypothesis that coefficient of Q4 in the population regression is zero. Use an alpha of .05. c) Interpret the result of the t-test from b). Pretend you are helping someone who knows little statistics understand what that 3.70 means. c) Please plot the residuals against time. Present the plot and explain what it tells you about the validity of the model of tourist arrivals presented here. The residuals, along with the data and the estimation, are in an Excel workbook: Fac-Stu\Bus\Easton\Ecn. 220\FinExmData.xls