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Stat 303: Section 505
Fall 2005
Form C
Final Exam
Instructor: Elizabeth Young
Instructions:
1.) Don’t EVEN open this until I tell you. (Meanwhile, read the rest of the
instructions.)
2.) Be SURE to mark your Form on the scantron!
3.) Sign your name on the line on the scantron. With this signature, you
agree to follow the Aggie Honor Code:
“An Aggie does not lie, cheat, or steal or tolerate those who do.”
4.) There are 20 multiple-choice questions, each worth 5 points. Please
mark your answers CLEARLY with a #2 pencil. Multiple marks will be
counted wrong.
5.) You have two hours to finish this exam. It is worth 25% of your final
grade.
6.) TURN IN this test form along with the Scantron!
7.) Good luck!
Use the following for the next 7 questions. Deborah’s Dairy Market sells both cottage cheese and ice cream. Deborah recently noticed that in months when the store sells more cottage cheese, it seems to sell more ice cream as well, on average. One of her aides was assigned to put this theory to the test. The aide’s analysis of sales data for the past twelve months (in gallons of ice cream and quarts of cottage cheese) gives the following SPSS output. (Cottage is the cottage cheese; it’s the explanatory variable .) Descriptive Statistics Mean Std. Deviation N ice_cream (^) 38.17 6.939 12 Cottage (^) 25.08 5.900 12 ANOVA(b) Model Sum of Squares Df Mean Square F Sig. 1 Regression (^) 486.999 1. Residual (^) 42.668 10 Total (^) 529.667 11 Coefficients(a) Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) (^) 9.879 2.714. Cottage (^) 2.473 .280 .959. 25 30 35 40 45 50 ice_cream 2 1 0
Regression Standardized Residual Dependent Variable: ice_cream Scatterplot
5.) The t-value for the slope was found to be significant, since we see that it has a p-value less than .001 from the chart. What are our conclusions in context of the problem? A.) Since the slope is significant, I can say that I am confident that as cottage cheese sales increase, ice cream sales also change (either increase or decrease). B.) Since the slope is significant, I can say with confidence that an increase in cottage cheese sales causes an increase in ice cream sales. C.) Since the slope is significant, I can say that I am not confident that as cottage cheese sales increase, ice cream sales also change. D.) Since the slope is significant, I can say that when ice cream sales increase, it causes an increase in cottage cheese sales as well. E.) More than one of the above are true. 6.) How would you interpret the slope that we found in context of the problem? A.) If the store sells one more quart of cottage cheese in a month, it will be predicted to sell 9.879 more gallons of ice cream in that month. B.) If the store sells one more quart of cottage cheese in a month, it will be predicted to sell 2.473 more gallons of ice cream in that month. C.) If the store sells one more gallon of ice cream in a month, it will be predicted to sell 9.879 more quarts of cottage cheese. D.) If the store sold 0 quarts of cottage cheese in a month, we might predict that it would sell 2.473 gallons of ice cream that month. E.) If the store sells 9.879 more gallons of ice cream in a month, it would be predicted to sell one more quart of cottage cheese. 7.) Santa Claus is worried that one of his elves might be sick because the elf seems to be producing toys at a slower rate today than usual. To find some hard evidence on the health of his elf, he sets up null and alternative hypotheses: Ho: The elf is producing toys at the same rate as usual. Ha: The elf is producing toys at a slower rate than usual. What would be an example of making a Type I error in this case? A.) Concluding that the elf is producing toys at the same rate as usual when he actually has slowed down. B.) Concluding that the elf is slower than usual when actually he is producing toys at the same rate. C.) Concluding that the elf is faster than usual when actually he is producing toys at the same rate. D.) Concluding that the elf is producing toys at the same rate as usual when he actually is producing toys at a faster rate. E.) Santa Claus is always good, so he would give the elf the day off, anyway.
8.) Mrs. Claus is worried that little girls don’t like to play with dolls any more, so she asks Santa about it. He has only taken Stat 303, so he decides to compare the average number of dolls he gives out in the decade 1996-2005 with the averages from the decades 1986-1995 and 1976-1985 (controlled for population growth, of course). What kind of hypotheses is he setting up? A.) Ho: μ 05 = μ 95 = μ 85 vs. Ha: μ 05 ≠ μ 95 ≠ μ (^85) B.) Ho: μ 05 = μ 95 = μ 85 vs. Ha: At least one decade has a different number of dolls given out from the other decades. C.) Ho: π 05 = π 95 = π 85 vs. Ha: π 05 ≠ π 95 ≠ π 85 D.) Ho: β 1 = 0 vs. Ha: β 1 < 0. E.) Ho: Number of dolls given out and decade are independent. 9.) The probability that a hurricane generated in the Atlantic around the equator makes landfall somewhere in the US is 0.35. What is the probability that the next two hurricanes generated in the Atlantic both hit landfall? A.) 0. B.) 0. C.) 0. D.) 0. E.) 0. Use the following to answer the next 5 questions. It is desired to test whether the brightness of three different brands of film are equal. To that end, random samples from 15 of the ratings from each brand were taken, and the following boxplot was generated: Kodak Fuji Agfa Brand Name 24 28 32 36 40 ColorBrightness
13.) What does the p-value of 0.009 mean in context of the problem? A.) The probability that we would conclude that the color brightness was different for the different brands of film when actually the color brightness was the same for all three brands is 0.009. B.) The probability of taking a random sample from three brands of film that had equal color brightness and getting sample means this different or even less different is 0.009. C.) The probability of taking a random sample from three brands of film that had equal color brightness and getting sample means this different or even more different is 0.009. D.) The probability that we would conclude that the mean color brightness was different for the three groups when in reality the color brightness is different for at least one of the groups is 0.009. E.) The probability that we would conclude that the mean color brightness was the same for all three groups when in reality it was different for at least one of the groups is 0.009. 14.) What is the definition of power in context of the F-test for equality of means? A.) Power is the probability I conclude that the color brightness for Fiji film is different from the color brightness for Kodak film and the brightness for Fiji film is also different from the color brightness for Agfa film when in reality all three have the same color brightness. B.) Power is the probability I conclude that the color brightness for all three types of film is the same when actually it is different. C.) Power is the probability I conclude the average color brightness for at least one of the three types of film is different from the others when in reality at least one is different. D.) Power is the probability I conclude that the color brightness for all three types of film is the same when in reality it is the same. E.) Power is the probability that I conclude that the color brightness for at least one of the three types of film is different from the others when in reality it is the same for all three groups.
Use the following to answer the next 3 questions. Even though Puerto Rico is a commonwealth of the United States, there are many cultural differences between the states on the continent and the island of Puerto Rico. These differences include the way consumers handle problems with purchases. Two researchers surveyed owners of VCRs in the Northeast U.S. and in Puerto Rico. They asked those who had experienced problems with their VCRs whether they complained. The results are given in the table below. Location Complained? United States Puerto Rico Yes 92 35 No 332 65 Chi-squared statistic = 7.797. 15.) What is the probability that a person from the United States who had problems with his VCR complained about it? A.) 0. B.) 0. C.) 0. D.) 0. E.) 0. 16.) We would like to run a chi-squared test on this data set. Which of the following is a range for the p-value based on the chart, and what conclusions do we make at the α =. significance level? A.) .0025 < p-value < .005, and we conclude that whether a person complains depends on where he is from. B.) .0025 < p-value < .005, and we conclude that where a person is from and whether he complains are not related. C.) .005 < p-value < .01, and we conclude that whether a person complains depends on where he is from. D.) .005 < p-value < .01, and we conclude that where a person is from and whether he complains are not related. E.) .005 < p-value < .01, but we cannot make a decision about whether to reject since we don’t know our hypotheses. 17.) Under the normal null hypothesis for a chi-squared test, what is the theoretical probability that a randomly selected person having trouble with his VCR both complained and was living in Puerto Rico? (No, the answer is NOT 35 / 524. Think about what we did in class – how did we develop the formula for expected value?) A.) 0. B.) 0. C.) 0. D.) 0. E.) 0.
Use the following to answer the next 3 questions. Independent random samples of 5 households in each of the four U.S. regions (Northeast, Midwest, South, and West) were taken, and the amount of energy each household consumed was measured. We are interested in assessing, at the 1% significance level, whether the data provide sufficient evidence to conclude that last year’s average energy consumption was different among the four U.S. regions. Assume that energy consumption in the four regions is normally distributed. Northeast Midwest South West Energy (^19) 17 15 13 11 9 7 5 Source Sum of Squares DF Mean Square F P -value Groups 95.017 6.41. Error 16 Total 174. 22.) What are the null and alternative hypotheses for using Analysis of Variance to analyze this data set? A.) H 0 : Energy consumption depends on region. Ha: Energy consumption and region are independent. B.) H 0 : μNE = μMW = μ (^) S = μ (^) W Ha: At least one of the regions has a mean energy consumption different from the other regions. C.) H 0 : Energy consumption and region are independent. Ha: Energy consumption depends on region. D.) H 0 :^ π^ NE =^ π^ MW =^ π^ S =^ π^ W Ha: At least one of the proportions of energy consumed is different. E.) H 0 : At least one of the regions has a mean energy consumption different from the other regions. Ha: μNE = μMW = μ (^) S = μ (^) W
23.) What is the estimate for the pooled variance of energy consumption for the four regions? A.) 31. B.) 79. C.) 95. D.) 4. E.) 16 24.) Which of the following statements about the energy consumption study is true? A.) It was an experiment, so we’re not worried about lurking variables. B.) It was only an observational study, so we should concerned about whether we can draw a cause and effect conclusion like, “Living in the Northeast or Midwest causes one to become an energy hog.” Maybe there’s a lurking variable, like outside temperature, that we should consider. C.) The sampling was done using a multistage sampling method. D.) Because the sampling was not done on every major city in each of the four regions, we cannot make inferences to the entire populations of the four regions of the US. E.) None of the above; we need more information about the study. 25.) Suppose we created a 95% confidence interval for mean length of time waiting for the bus of (3.12, 8.54) minutes, from our sample mean wait time of 5.83 minutes. Which of the following statements are true? A.) 95% of the time, the true mean μ length of time spent waiting for the bus will fall in the interval I selected above. B.) The probability that the interval I selected above contains 5.83 is 0.95. C.) If I were to repeat the study by keeping track of how long I wait for the bus multiple semesters, about 95% of the time, I would capture the true mean length of time spent waiting for the bus. D.) About 95% of the confidence intervals that I create will contain the mean 5. minutes. E.) The probability that the interval I selected above contains the true mean wait time for the bus is 0.95. Answers: 1.) D 2)D 3) D 4) C 5) A 6) B 7) B 8) B 9) A 10) D
- E 12) A 13) C 14) C 15) B 16) C 17) C 18) D 19) E 20) E
- C 22) B 23) C 24) B 25) C
