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Stat 303: Section 503
Spring 2006
Form A
Exam 2
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.) Be sure to turn in your scantron, cheat sheet, and this exam form!
6.) This exam is worth 20% of your grade.
7.) Good luck!
1.) If Acie Law makes 32.7% of his 3 point attempts for his entire career, what is the probability that he makes at least 34.4% of his 96 attempts this season? A) 0. B) 0. C) 0. D) 0. E) 0. Use the following for the next two questions: In the recent game against that school in Austin, Acie Law shot three 3 pointers, making one of them. Assuming that he makes 34.4% of his 3 point attempts this season, and that each shot is independent, here is the probability distribution of X, where X is the number of three pointers made if Acie is given the ball. X = number of 3 pointers made
P(X) .282 .444 .233.
2.) How many of the three point shots would we have expected Acie to make against t.u.? What is the variance of the number of three point shots Acie makes (out of 3)? A) Expected: 1 Variance: 1. B) Expected: 1.033 Variance: 0. C) Expected: 1.033 Variance: 1. D) Expected: 1.5 Variance: 0. E) Expected: 1.5 Variance: 1. 3.) What is the probability that two randomly selected 3 point shots both make it in? A.) 0. B.) 0. C.) 0. D.) 0. E.) 0.
7.) Suppose a researcher is interested in testing the hypotheses Ho: true mean = 4 vs. Ha: true mean ≠ 4. Her test statistic is 0.6026. What is her p-value? A.) 0. B.) 0. C.) 0. D.) 0. E.) 0. 8.) Suppose a researcher wishes to test the hypotheses Ho: true mean = 3 vs. Ha: true mean > 3. He finds in a sample of 75 experimental units a sample mean of 4.63, and he knows that σ = 2.12. What is his test statistic for this study? A.) 0. B.) 2. C.) 1. D.) 6. E.) 0. 9.) Why do we call the distribution of the sample proportion, p, a sampling distribution? A.) Because it’s the distribution of the sample of random observations. B.) Because it’s the distribution of the proportion of the samples. C.) Because we relate all the sample proportions to a distribution. D.) Because we sample from the distribution to find the sample proportion. E.) Because we can’t get the distribution of all the sample proportions, only samples. 10.) Suppose we know that X ~ N(3, 5^2 ) and Y ~ N(2, 12^2 ). What is the distribution of X + Y? A.) N(5, 17^2 ) B.) N(5, 13^2 ) C.) N(5, 15^2 ) D.) N(5, 16^2 ) E.) N(5, 18^2 )
11.) An agronomist interested in the effect of a new herbicide on cotton plants decided to test whether the new herbicide was better than or worse than the old pesticide. He sets up hypotheses Ho: mean yield of cotton plants on new pesticide = 68.75 vs. Ha: mean yield of cotton plants on new pesticide ≠ 68.75. He finds a sample mean of 76.32, with a corresponding p-value of 0.0846 for this test. Which of the following is true about confidence intervals for the mean yield of cotton plants on the new pesticide? A.) The 99% confidence interval will include 76.32, but the 95% confidence interval won’t. B.) The 95% confidence interval will not include 76.32, and neither will the 90% confidence interval. C.) The 95% confidence interval will include 68.75, but the 90% confidence interval won’t. D.) The 95% confidence interval will include 68.75, and so will the 99% confidence interval. E.) The 95% confidence interval will not include 68.75, and neither will the 90% confidence interval. 12.) Which of the following best describes random sampling? A.) All possible observations are equally spread out in the sample. B.) All possible samples of size n are equally likely to be chosen. C.) The sample results in a test statistic with a normal distribution. D.) All possible observations are normally distributed in the sample. E.) All possible samples of size n are equally spread out. 13.) A doctor wishes to find out whether patients on her new diet plan have a lower average cholesterol level than patients on the old diet. (Patients on the old diet average 167.4.) As part of her study, she creates a 95% confidence interval for patients on this diet plan of (148.5, 179.3). (The sample mean was 163.9.) Which of the following is true about this confidence interval? A.) 95% of the confidence intervals like this one that doctors create will contain 163.9. B.) 95% of the confidence intervals like this one that doctors create will contain the true average cholesterol level of patients on the new diet. C.) The doctor can be 95% confident that the interval (148.5, 179.3) contains the mean 167.4. D.) The doctor can be 95% confident that the interval (148.5, 179.3) contains the mean 163.9. E.) 95% of the confidence intervals like this one that doctors create will contain the sample mean cholesterol level of patients on the new diet. 14.) Suppose we tested Ho: μ = 12 vs. Ha: μ > 12 at α = 0.01 and got a p-value of 0.0623, but in reality, the mean is actually 13. Which of the following would be true?
μ < 1000, with an x^ = 998.4 and a sample size of 55,000 women across the US, the p- value was 0.00134. What can we say about this study? A.) The null hypothesis was not rejected, so we have no evidence that women are scoring lower than men on the SAT. B.) Because the sample size is so large, I’m bound to get statistical significance, but 998.4 isn’t practically different from 1000. C.) Because the sample size is so large, statistical significance is expected, so the p- value of 0.00134 means that we are sure at the 0.01 level of significance that women are scoring practically significantly lower than 1000. D.) If women from households with lower income levels scored much lower on the SAT than women from households with higher income levels, we would be sure that income was a lurking variable, and so we should take that into account. E.) Male chauvinist pigs write the SAT!!! Clearly, it is biased against women!! 19.) Suppose 32% of the students at A&M believe the bus system is running smoothly these days. I took a sample of 1,000 students, and found that 38% of the students in my sample believed the bus system was running smoothly. What distribution will my sample proportion, p, have? A.) p ~ N (0.32, 0.0147^2 ) B.) p ~ N (0.32, 0.0153^2 ) C.) p ~ N (0.38, 0.0147^2 ) D.) p ~ N (0.38, 0.0153^2 ) E.) We can’t say, since we don’t know whether nπ ≥ 15 and n(1-π) ≥ 15. 20.) Which of the following statements are false? A.) The probability of all possible events always adds up to 1. B.) A p-value is always a probability. C.) If we take a large enough sample from the population, P( x < c) will always be approximated by the normal distribution. (For any c.) D.) If we keep repeating the same experiment, the distribution of the sample proportions will always approach the normal distribution. E.) None of the above is false. 1E 2B 3E 4A 5A 6D 7C 8D 9C 10B 11E 13B (Note that C is wrong because that interval actually does contain 167.4.) 14E 15A 16B 17B 18b 19A 20D
