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STA2023- Spring 2013 - Ripol EXAM 2 April 2, 2013 Instructions: This exam contains 33 Multiple Choice questions. Please select the best answer among the alternatives given. Each question is worth 3 points, for a total of 99 points. The last point will be awarded for correctly bubbling in your name, UFID number and Test Form Code on the scantron sheet and showing your GatorOne picture ID. YOU MUST SIGN, IN INK, the Honor Pledge on the next page of the exam and the back of the scantron sheet. The proctors will compare them to the signature on the ID. You may write whatever you want on this test, but only the answers bubbled in the scantron sheet will be graded. Make sure you mark all your answers on this test so you can compare your answers to the key that will be posted on the course website. This page contains Tables and Formulas. You may detach this page from the exam but make sure the rest of the exam does not fall apart! Case one mean one prop. parameter p estimator standard error Estimate of stderr x s n p̂ p(1 p) n n CI: ST: pˆ (1 pˆ ) n p0 (1 p0 ) n Sampling Distribution t (n-1) z STA2023- Spring 2013 - Ripol EXAM 2 TEST FORM A April 2, 2013 Honor pledge: "On my honor, I have neither given nor received unauthorized aid on this examination." SIGN your name in this box in INK Write your UFID number . In the Fall of 2012 there were 1401 applicants to UF’s Medical School. Only 217 of them were accepted. We can use this data to estimate UF’s Medical School admissions rate with a 95% confidence interval for the proportion admitted in all years. 1. Which of the following assumptions do we need to make? a) Students were randomly selected to apply to UF’s Medical School that year. b) UF’s Medical School used a random process to determine which students to admit. c) UF’s Medical School’s admissions rate is representative of all medical schools. d) The admissions rate for 2012 is representative of all years at UF’s Medical School. e) All of the above. 2. The population proportion is: a) 217 b) 1401 c) 15.49% d) 95% e) unknown 3. The point estimator for the population proportion is: a) 217 b) 1401 c) 15.49% d) 95% e) unknown 4. The margin of error for the 95% confidence interval for p, UF’s Medical School admissions rate is: a) 0.00009 b) 0.00967 c) 0.00018 d) 0.01895 e) 0.09834 A recent national poll found that 63% of Americans believe in an immigration reform that would allow a path to citizenship for illegal immigrants who meet certain requirements. The 95% CI for p was: (0.616, 0.644). Determine if each of the following statements are True or False. 5. The probability that p is included in a 95% confidence interval is .95. a) True b) False 6. 95% of all Americans believe that between 62% and 64% of illegal immigrants a) True b) False will meet the requirements for citizenship. 7. We are 95% confident that the proportion of Americans in the sample that a) True b) False believes in a path for citizenship for illegal immigrants is between 62% and 64%. 8. We are 95% confident that the proportion of all American that believes in a path a) True b) False for citizenship for illegal immigrants is between 62% and 64%. 9. There is a 95% probability that the proportion of all Americans that believes in a a) True b) False path for citizenship for illegal immigrants is between 62% and 64%. 10. Which of the following statements is true? a) The center of a confidence interval is a population parameter. b) The bigger the margin of error, the smaller the confidence interval. c) The confidence interval is a type of point estimate. d) A population mean is an example of a point estimate. e) None of the above statements are true. 11. A researcher wants to estimate the average number of daily users of a computer server. He estimates the standard deviation to be around 500. Which of the following sample sizes is the smallest that will give a margin of error of 100, with 95% confidence? a) 95 b) 100 c) 196 d) 500 12. During the Million Minutes of Reading campaign elementary school students are encouraged to record how many minutes they read every day for a month. A random sample of 5th grade students was selected, and their total number of minutes for the month was recorded: 454, 617, 1785, 545, 583. Construct a 95% confidence interval for µ. a) (309.7, 1283.9) b) ( 82.4, 1511.2) c) ( 25.4, 1586.2) d) (157.8, 1435.8) e) (106.8, 1486.8) 13. Are the assumptions necessary for the validity of this confidence interval satisfied? a) No, the assumptions are clearly violated so we should not have made the interval in the first place. b) It’s impossible to check some of the assumptions, so we should always mention them in our conclusions.. c) We can only extend the conclusions to those five students, not to the general population of 5th graders. d) The assumptions seem to be satisfied, since the problem states the students were a random sample. e) The validity of the confidence interval does not depend on the assumptions – it’s a separate issue. 14. A random survey of 50 high school students revealed that 14 of them admitted to having stolen something within the previous year. Can we use this data to construct a 95% CI for the population proportion? a) No – the sample size is too small. b) Yes – there are more than 30 observations in the sample. c) Yes – but we have to add two successes and two failures to the data. d) Yes – but we have to add one success and one failure to the data. e) No – a confidence interval here would be for the sample proportion, not the population proportion. 15. If we wanted to test whether more than 25% of high school students have stolen something within the previous year, how would we write the null and alternative hypotheses? a) Ho: p =.25 Ha: p > .25 b) Ho: p̂ =.25 Ha: p̂ > .25 c) Ho: p =.25 Ha: p̂ = .28 d) Ho: p̂ =.25 Ha: p = .28 e) Ho: p̂ =.28 Ha: p̂ > .25 16. For the Sampling Distribution of p-hat to be Normal we will need a larger sample size when: a) p is very small b) p is very large c) p is close to 0.5 d) p is close to 30 e) p is far from 0.5 17. The Sampling Distribution of x-bar will be approximately Normal: a) only if the sample size is 30 or more b) only if the population size is 30 or more c) only if the shape of the original distribution is Normal d) only if the shape of the sample distribution is Normal e) none of the above 18. Which of the following is the best value from the Z table to use in making a 93% confidence interval? a) 1.78 b) 1.79 c) 1.80 d) 1.81 e) 1.82 19. When testing Ho: p =.15 vs Ha: p ≠ .15 the test statistic turns out to be z = 2.72. The p-value for this test is: a) 0.9967 b) 0.0033 c) 0.0066 d) 0.9934 e) 0.4967 Nutritionists recommend monitoring the intake of fat for a variety of health reasons, including weight control. For male, middle-aged Americans, the distribution of daily fat intake is said to have a mean of 37 grams and a standard deviation of 32 grams. We will select a random sample of 45 male, middle-aged Americans, measure their fat intake and compute the sample mean. 20. What is the Sampling Distribution of the sample mean? a) The sample mean is just one number so it does not have a distribution. b) The sampling distribution of x is approximately Normal because the sample size is large. c) The sampling distribution of x is not Normal because we cannot go three standard deviations to the left. d) The sampling distribution of x is Normal because the original distribution is Normal. e) The sampling distribution of x is skewed because the original distribution is skewed. 21. Find the probability that the average fat intake for our sample of male, middle-aged Americans is less than 30 grams. a) 0.3594 b) 0.4129 c) 0.5871 d) 0.9292 e) 0.0708 Some companies claim to offer coaching courses that can improve your SAT scores. SAT Math scores in the absence of coaching have a mean of 475 points. After a very successful advertising campaign, a company gets 10,000 customers, whose average SAT Math score after coaching turns out to be 478 with a standard deviation of 100 points. We will use this data to construct a confidence interval for . 22. In this problem, represents the average SAT Math score: a) for all students in the absence of coaching, which is 475 points. b) for all students taking this course, which is 478 points. c) for all students not taking this course, which is unknown. d) for all students that could have taken this course, which is unknown. e) for all students in the sample population, which is unknown. 23. The standard error of the statistic is: a) very small since the sample size is so large b) very large since the sample size is so large c) very small since the effect of the course is so small d) very large since the effect of the course is so small e) unrelated to either the sample size or the effect of the course 24. The 95% confidence interval for is (476, 480). Based on this interval we can say that the course: a) improves average SAT Math scores, but not enough to make a difference in college admissions. b) does not improve average SAT Math scores at all. c) improves SAT Math scores for 95% of all students, but not for the other 5%. d) makes a big enough difference in the SAT Math scores for college admissions for 95% of students. e) may or may not make a difference in average SAT Math score – the results are inconclusive. 25. When testing Ho: p =.62 vs Ha: p < .62 the data collected gives 49 successes out of 100. What is the standard error that should be used in computing the test statistic? a) 0.0485 b) 0.4999 c) -2.60 d) -2.68 e) -0.13 26. Suppose that 10% of items produced by an assembly line are defective. We will take a random sample of 250 of these items and count the number of defectives in the sample. How would you find the probability that more than 12% in the sample are defective? a) Find the area to the right of 0.12 on a Normal curve. b) Find the area to the right of 0.33 on a Normal curve. c) Find the area to the right of 0.02 on a Normal curve. d) Find the area to the right of 1.05 on a Normal curve. e) none of the above 27. This problem is an example of: a) sampling distribution b) statistical inference c) confidence interval d) significance test e) sample size determination 28. The figures 10% and 12% in this story are: a) both parameters b) both statistics c) a parameter and a statistic respectively d) a statistic and a parameter respectively e) none of the above 29. When testing Ho: p =.75 vs Ha: p < .75 the sample proportion of successes turns out to be 0.77. The p-value for this test is: a) greater than 0.50 b) smaller than 0.50 c) equal to 0.50 d) equal to 0.02 e) impossible to determine 30. When testing Ho: p =.62 vs Ha: p < .62 the data collected gives 49 successes out of 100. We can conduct the significance test because: a) there are more than 30 observations in the sample b) there are 49 successes and 51 failures in the sample c) there are 62 successes and 38 failures expected under the null hypothesis d) there are more than 50 successes and 50 failures in the population e) there are more than 15 successes and 15 failures in the population 31. If the p-value of a test is 0.014 then: a) we can reject the null hypothesis at α =.10 and .05 but not .01 b) we can reject the null hypothesis at α =.01but not .10 and .05 c) we can reject the alternative hypothesis at α =.10 and .05 but not .01 d) we can reject the alternative hypothesis at α =.01but not .10 and .05 e) we can reject the alternative hypothesis at α =.10 and the null at α =.01 32. If the p-value of a test is 0.96 then there is: a) a lot of evidence to reject the null hypothesis c) no evidence to reject the null hypothesis e) no evidence to reject the alternative hypothesis b) some evidence to reject the null hypothesis d) a lot of evidence to reject the alternative hypothesis 33. If the results are statistically significant at α = .05 then: a) we reject Ho at α = .05 b) the p-value was larger than .05 c) the test statistic was positive d) all of the above e) none of the above