STAT 301 Extra Practice EXAM QUESTIONS AND ANSWERS

STAT 301 Extra Practice EXAM QUESTIONS AND ANSWERS 1. Which of the following represents measures of center? A. IQR, Mode, Range B. Mean, Median, Standard Deviation C. IQR, Mean, Median D. Mean, Median, Mode 2. Which of the following represents measures of spread? A. IQR, Mode, Range B. IQR, Range, Standard Deviation C. IQR, Mean, Median D. Mean, Median, Mode 3. Identify the implied population and the sample from the following situation: CNN and USA Today ran a national survey by interviewing 1800 registered voters across the nation. They found that 44% of those polled were college graduates. A. Population—All registered voters in the U.S.; Sample—792 people surveyed B. Population—1800 adults in the U.S.; Sample—792 people surveyed C. Population—All adults in the U.S.; Sample—1800 people surveyed D. Population—All registered voters in the U.S.; Sample—1800 people surveyed 4. What does the term standard deviation mean? A. Measure of center B. Distance from Q1 to Q3 C. Typical distance away from the mean D. Typical distance away from the median 5. If you have found that a distribution is skewed left, which of the following answers best describes the distribution? You have the following data: x  139 , s = 13, 5 # Summary: 119, 130, 140, 150, 158. A. Center = 139, Spread = 13 B. Center = 139, Spread = 20 C. Center = 140, Spread = 13 D. Center = 140, Spread = 20 6. With the histogram at the right, what general shape does it have? A. Bimodal B. Approximately symmetrical C. Skewed Left D. Skewed Right 7. With the histogram at the right, what general shape does it have? A. Bimodal B. Approximately symmetrical C. Skewed Left D. Skewed Right *** ATA and Proline are two stocks traded on the New York Stock Exchange. For the past six weeks, the Friday closing price for each stock ($/share) has been: ATA: 19 18 21 22 21 23 Proline: 6.2 6.2 6.9 6.2 7.2 7.4 8. Compute the mean closing price for ATA. A. 19 B. 23 C. 20.67 D. 22.90 9. Compute the median closing price for Proline. A. 6.2 B. 6.88 C. 7.6 D. 6.55 10. Compute the mode of closing prices for Proline. A. 6.2 B. 6.88 C. 7.6 D. 6.55 11. Compute the sample standard deviation for ATA. A. 1.86 B. 2.05 C. 5 D. 3.47 *** Advantage VCR’s carry a one year warranty. However, the terms of the warranty require that a registration card be sent in. One of the questions on the registration card asks the owner’s age. For a random sample of 30 registration cards, the ages were: 38 27 41 31 31 35 21 36 37 32 45 47 32 26 23 19 27 38 47 51 52 65 46 33 27 22 25 27 31 34 12. Find the value of A. 41 Q1. B. 27 C. 19 D. 32.5 13. Find the value of the median. A. 32 B. 32.5 C. 33 D. 33.5 14. Find the value of the IQR. A. 12 B. 13 C. 14 D. 15 15. Find the RANK of Q3. A. 8th number B. 15.5 C. 23rd number D. 41st number 16. Find the value of Q3. A. 23 B. 34.9 C. 10.6 D. 41 17. You roll 2 fair dice, one red and one green. What is the probability of rolling a 2 on the red die and a 6 on the green die? A. 12 36 B. 2 5 C. 36 D. 36 *** A real estate office surveyed a random sample of 70 clients. One question asks if the client is satisfied or not and another asks if the client was referred to the company by another client. Results of the survey are shown in the following table. Referred Not Referred Total Satisfied 25 25 50 Not Satisfied 5 15 20 Total 30 40 70 If a client is selected at random (from this group of 70 clients), find: 18. The probability the client is satisfied. A. 25 50 B. 30 50 C. 30 70 D. 50 70 19. The probability the client is satisfied and was referred. A. 25 30 B. 25 50 C. 25 70 D. 30 70 20. The probability the client is satisfied, given the client was referred. A. 25 30 B. 25 50 C. 30 50 D. 30 70 21. Are the events “the client is satisfied” and “the client was referred” independent and/or mutually exclusive? A. Yes independent and Yes Mutually Exclusive B. Yes independent but No, not Mutually Exclusive C. No, not independent, and No, not Mutually Exclusive D. No, not independent, but Yes, Mutually Exclusive *** A bowl contains 8 M&Ms: 4 brown, 3 green, and 1 yellow. 22. What is the probability that you will draw a green one on the first draw? A. 0.5 B. 0.125 C. 0.375 D. 0.75 23. What is the probability of drawing a green one on the 1st draw and a brown one on the 2nd draw, without replacement? A. 0.214 B. 0.375 C. 0.250 D. 0.571 24. What is the probability of drawing a green one on the 1st draw and a brown one on the 2nd draw, with replacement? A. 0.1875 B. 0.2143 C. 0.375 D. 0.5 25. What is the probability that you will draw a brown one or yellow one on the first draw? A. 0.875 B. 0.625 C. 0.5 D. 0.375 *** You draw one card from a standard deck of 52 cards. 26. What is the probability that the card is a Queen? A. 13 52 B. 52 C. 52 D. 52 27. What is the probability that the card is a Queen or a Diamond? A. 16 52 B. 52 C. 17 52 D. 15 52 *** Totum is a chain of small grocery stores in Nebraska. From data kept over the last ten years, the franchise operators have determined the following probabilities for the number of bad checks passed in a store each week: Number of Bad Checks = x 0 1 2 3 4 5 Probability = P(x) 0.3 0.3 0.2 0.1 0.05 0.05 28. Find the probability of less than 3 bad checks. A. 0.05 B. 0.1 C. 0.8 D. 0.9 29. What is the expected number of bad checks? A. 1 B. 1.45 C. 1.75 D. 2 *** An insurance company says 10% of all fires are caused by arson. A random sample of ten insurance claims for fires is under study. 30. Find the expected number of insurance claims for fires caused by arson. A. 0.10 B. 10 C. 1.0 D. 0.90 31. Find the standard deviation of the number of insurance claims for fires caused by arson. A. 0.425 B. 0.949 C. 0.09 D. 1.0 32. Find the probability that none of the fires are caused by arson. A. 0.000 B. 0.100 C. 0.900 D. 0.349 33. Find the probability that exactly six of the 10 fires are caused by arson. A. (0.10)6(0.90)6 B. 210 (0.10)6(0.90)4 C. (0.10)4(0.90)6 D. 10 (0.10)6(0.90)4 34. Find the probability that three to six (including three and six) of the fires are caused by arson. A. 0.070 B. 0.999 C. 0.321 D. 0.987 *** The incubation time for New Hampshire Redd Chicks is normally distributed with mean = 25 days and standard deviation = 3 days. Use the Empirical Rule to answer the following questions. 35. What percentage of the chicks will hatch in 22 to 28 days? A. 68% B. 95% C. 99.7% D. 47.5% 36. What percentage of the chicks will hatch in 16 to 34 days? A. 68% B. 95% C. 99.7% D. 47.5% 37. Assume the average SAT math score is 500 with a standard deviation of 100. What score do you need to be in the top 8 % of test takers (to the nearest point)? A. 359 B. 584 C. 640 D. 641 38. Quality control for KPS DVRs has shown that a certain model has a normal distribution with a population mean life of 5.5 years and a standard deviation of 0.8 years. Using this information, how long should the guarantee period be if the company wishes to replace no more than 7% of the DVRs during the guarantee period? (to the nearest tenth of a year) A. 4.3 B. 4.7 C. 5.9 D. 6.3 *** The snow pack on the summit of Wolf Creek Pass, Colorado on March 1 has been measured for many years by the National Weather Bureau. The depth of the snow pack in inches is normally distributed with a mean of 75 inches and a standard deviation of 10 inches. For a given, year, find: 39. the probability that the snow pack will be more than 85 inches. A. 0.1587 B. 0.3413 C. 0.6826 D. 0.8413 40. the probability that the snow pack will be between 68 and 78 inches. A. 0.2420 B. 0.3759 C. 0.3821 D. 0.6179 41. Systolic blood pressures in a particular population are normally distributed with mean equal to 115 and standard deviation equal to 12 (in mmHg). What is the probability that an individual selected at random has blood pressure between 98 and 133? (a) 0.0778 (b) 0.8554 (c) 0.9332 (d) Cannot be solved 42. Refer to the data in the previous question. What is the probability that the sample mean of 16 measurements is between 118 and 123? (a) 0.1549 (b) 0.8413 (c) 0.9962 (d) Cannot be solved *** Below are the team by team statistics on home runs hit by MLB teams during the early part of 1994. 43. Which of the following is a correct statement? A) The American League plot is reasonably symmetric. B) The National League plot is skewed to the left. C) The median number of home runs hit by the NL was higher than by the AL. D) All of the above. 44. Following a dramatic drop of 500 points in the Dow Jones Industrial Average in September 1998, a poll conducted for the Associated Press found that 92% of those polled said that a year from now their family financial situation will be as good as it is today or better. The number 92% is a (a) Parameter (b) Population (c) Sample (d) Statistic 45. If the confidence level increases, which of the following must also increase? (a) sample size (b) zα/2 or tα/2 (as applicable) (c) standard deviation (d) sample statistic / point estimate 46. You want to estimate the mean SAT score for a population of students with a 90% confidence interval. Assume that the population standard deviation is  = 100. If you want the margin of error to be approximately 10, you will need a sample size of (a) 30 (b) 271 (c) 385 (d) 1083 47. The water diet requires one to drink two cups of water every half hour from when one gets up until one goes to bed, but otherwise allows one to eat whatever one likes. Four adult volunteers agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The weights (in pounds) are Person 1 2 3 4 Weight before the diet 180 125 240 150 Weight after six weeks 170 130 215 152 To determine if the diet leads to weight loss, we test the hypotheses below at α = .05 H0: d = 0, H1: d > 0. where d = Weight Before – Weight After Based on these data we conclude that (a) The water diet works because we have significant evidence. (b) The water diet works because we do not have significant evidence. (c) The water diet does not work because we have significant evidence. (d) The water diet does not work because we do not have significant evidence. 48. A study of iron deficiency among infants compared samples of infants following different feeding regimens. One group contained breast-fed infants, while the children in another group were fed a standard baby formula without any iron supplements. The researchers suspect breast-fed babies will have higher iron. Here are the results on blood hemoglobin levels at 12 months of age. Group n x s Breast-fed 23 13.3 1.7 Formula 19 12.4 1.8 Based on these data our p-value is (a) 0.025 < p-value < 0.050 (b) 0.050 < p-value < 0.075 (c) 0.075 < p-value < 0.100 (d) 0.100 < p-value < 0.150 49. The FDA tests drugs for safety and assumes that all drugs are unsafe until evidence is provided to suggest otherwise. A new drug for minor skin irritation was tested at a level of significance of .01. The drug could have lethal side effects. Identify which error is more dangerous, along with its correct description. (a) Type I is more dangerous, which would be thinking the drug is safe, but it really is not. (b) Type I is more dangerous, which would be thinking the drug is not safe, but it really is. (c) Type II is more dangerous, which would be thinking the drug is safe, but it really is not. (d) Type II is more dangerous, which would be thinking the drug is not safe, but it really is. 50. All but one of the following statements contains a blunder. Which statement is correct? (a) The correlation between planting rate and yield of corn (in bushels) was found to be r = 0.23. (b) The correlation between the gas mileage of a car and its weight is r = 0.71 MPG. (c) We found a high correlation (r = 1.09) between the height and age of children. (d) We found a correlation of r = –.63 between gender and political party preference. 51. The quality-control supervisor wishes to estimate the mean weight of 5,500 packages of raw material. A random sample of 250 packages yields a mean of 65 pounds. The population standard deviation is 15 pounds. Find a 90% confidence interval for the unknown population mean. (a) 63.14 to 66.86 (b) 63.44 to 66.56 (c) 64.67 to 65.33 (d) 61.10 to 68.90 52. What is the primary purpose of a 95% confidence interval for a mean? (a) to estimate a sample mean (b) to test a hypothesis about a sample mean (c) to estimate a population mean (d) to provide an interval that covers 95% of the individual values in the population 53. A researcher asked random samples of 50 kindergarten teachers and 50 12th grade teachers how much money they spent out-of-pocket on school supplies in the previous school year, to see if teachers at one grade level spend more than the other. A 95% confidence interval for μ1−μ2 is $30 to $50, where μ1 and μ2 are the population means for the amount spent by kindergarten and 12th grade teachers, respectively. Based on this result, it is reasonable to conclude that (a) 95% of all kindergarten and 12th grade teachers spend between $30 and $50 on average. (b) 95% of all kindergarten teachers spend between $30 and $50 more than 95% of all 12th grade teachers. (c) Kindergarten teachers spend more on average than do 12th grade teachers. (d) 12th grade teachers spend more on average than do kindergarten teachers. 54. You want to design a study to estimate the proportion of students on your campus who agree with the statement, “The student government is an effective organization for expressing the needs of students to the administration.” You will use a 95% confidence interval and you would like the margin of error to be 0.05 or less. The minimum sample size required is approximately (a) 30 (b) 271 (c) 385 (d) 1083 55. A manufacturer of electrical products will not accept a shipment of a certain part from a vendor if there is a reason to believe that the mean resistance is not 70 ohms. A random sample of 35 parts selected from a large shipment yields a mean of 68 ohms. The population standard deviation is assumed to be 10 ohms. The observed p-value of the test is: (a) 0.0381 (b) 0.1190 (c) 0.2380 (d) 0.9619 56. Suppose the following information was collected, where X = year, and Y = # of antelope per square mile. X 1 2 3 4 5 6 7 8 Y 2.9 2.4 2.0 2.3 3.2 2.9 3.4 2.8 Find the LSR equation of the line of best fit. (a) y = 2.3143 + 0.0940x (b) yˆ = 2.3143 + 0.0940x (c) y = .0940 + 2.3143x (d) yˆ = 0.940 + 2.3143x 57. Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights actually vary slightly from bag to bag and are normally distributed with mean  . A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses H0:  = 14, H1:  < 14. To do this, he selects sixteen bags of this brand at random and determines the net weight of each. He finds the sample mean to be x = 13.82 and the sample standard deviation to be s = 0.24. The conclusion should be: (a) Fail to reject H0 because the p-value > 0.125 (b) Fail to reject H0 because the p-value > 0.250 (c) Reject H0 and accept HA because the p-value < 0.010 (d) Reject H0 and accept HA because the p-value < 0.005 ANSWERS # ANS # ANS # ANS 1 D 20 A 39 A 2 B 21 C 40 B 3 D 22 C 41 B 4 C 23 A 42 A 5 D 24 A 43 D 6 D 25 B 44 C 7 B 26 C 45 B 8 C 27 A 46 B 9 D 28 C 47 D 10 A 29 B 48 B 11 A 30 C 49 A 12 B 31 B 50 A 13 B 32 D 51 B 14 C 33 B 52 C 15 C 34 A 53 C 16 D 35 A 54 C 17 C 36 C 55 C 18 D 37 D 56 B 19 C 38 A 57 D