Source gap (S0516): Source interface note: The original widget displays a countdown (89:48 in the first capture) and a “Reset Exam” control. The captures do not show introductory test instructions or an explicit starting time. The final capture shows “Check Answers,” but no checked answer, score, key, or feedback state is recorded.
1. A sample of 223 students were asked about their choice of profession. The information obtained is given in the table below. What percentage of students want to be a doctor?
Profession Sex: Female Sex: Male College Professors 23 18 Doctor 19 35 Engineer 17 29 Musician 8 12 Other 34 28
A. 0.453B. 0.206C. 0.242D. 0.295E. 0.278
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2. 500 students sat in for a university admission exam. The grading system is as follows: A: Over 80%, B: 61%–80%, C: 41%–60%, D: 21%–40%, F: 0%–20%. The following pie chart shows the proportions of students that fall into each grade. If the total marks of the exam is 340, how many students obtained at least 60%?
Pie chart of exam grades: Over 80% is 17%; 61 to 80% is 32%; 41 to 60% is 26%; 21 to 40% is 17%; 0 to 20% is 6%. The five sectors use pink, blue, purple, gray, and white respectively. Open full-size image S0517
Grade range in the chart Percentage shown Over 80% 17% 61 to 80% 32% 41 to 60% 26% 21 to 40% 17% 0 to 20% 6%
Source gap (S0517): Source inconsistency: The five displayed percentages total 98%. The source also asks about “at least 60%” while its grade ranges divide at 60%/61%. Both are retained as captured.
A. 255B. 130C. 300D. 246E. 204
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3. A student was asked to record the height (in ft) and weight (in lb) of her classmates by her teacher. Using the measurements she obtained, she was then asked to calculate the coefficient of correlation between height and weight from the data. Her result was 0.834. However, a defect was found in the weight scale that added an extra 10 lb to each weight. If the average weight of the students is 127 lb, what statement is true for the correlation coefficient?
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4. The null hypothesis, H 0 : μ = 4 H_0:\mu=4 H 0 : μ = 4 H a : μ < 4 H_a:\mu<4 H a : μ < 4
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5. In a study, 12 newly born twin lambs were divided in two groups. One of the twins was fed a special diet, while the other was fed a regular diet. After 5 months, their weights were measured. What kind of test should the researcher use to assess the effect of the special diet?
A. One sample t-testB. Paired t-testC. Two sample t-testD. Two sample z-testE. None of the above
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6. In a clinical trial, two groups of patients with a particular skin disease under their elbow were studied. One group was given a new drug. The other group was given a placebo. Patients of both groups were made aware of the type of drug given to them. After 2 weeks, the area covered by the infection is measured again. The difference in the measures were taken to be the responses. Which statement is true for this experiment?
A. The new drug should have been compared to another brand that was known to workB. There is no replicationC. There is no randomizationD. The time length should have been longer than 2 weeksE. There is bias and confounding present
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7. A company claims to produce light bulbs with an average lifetime of 50 weeks with a standard deviation of 4. 100 bulbs were taken and their lifetimes were measured over a long period of time. What can the smallest possible value of the sample mean be, so that we can reject the null hypothesis, H 0 : μ = 50 H_0:\mu=50 H 0 : μ = 50 H a : μ > 50 H_a:\mu>50 H a : μ > 50
A. 50.25B. 49.18C. 50.66D. 50.62E. 50.54
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8. Consider the following fitted model: y ^ i = 143.56 + .512 x i − 23.4 d i \hat y_i=143.56+.512x_i-23.4d_i y ^ i = 143.56 + .512 x i − 23.4 d i y ^ i \hat y_i y ^ i x i x_i x i d i d_i d i
I. The average expenditure is higher in the female group than in the male group.
II. For the female group, the average expenditure is 23.4 times that of the male group.
III. For both sexes, a unit increase in income results in a .512 unit increase in expenditure.
A. Only IB. I and IIC. II and IIID. I and IIIE. I, II, and III
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9. For the following Normal probability distribution, what is the approximate probability of the shaded area?
Normal density curve centered at x=50, with horizontal ticks 20, 30, 40, 50, 60, 70, 80 and vertical ticks from 0 to 0.04. The area under the curve to the left of x=40 is shaded pink. Open full-size image S0522 A. 0.32B. 0.16C. 0.11D. 0.25E. Cannot be determined
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10. The dotplot above displays the number of cookies in 20 bite-size cookie packages. Which below answer is approximately the mean number of cookies per package?
Dotplot titled Number of Cookies, with ticks 9 through 16: 2 packages at 10 cookies, 4 at 11, 2 at 12, 5 at 13, 3 at 14, and 4 at 15; there are no dots at 9 or 16. Open full-size image S0523
Number of cookies Number of dots (packages) 9 0 10 2 11 4 12 2 13 5 14 3 15 4 16 0
A. 9 cookiesB. 11 cookiesC. 13 cookiesD. 15 cookiesE. 17 cookies
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11. A study of birthweights of infants in North Korea and South Korea was conducted from two independent random samples of babies in the two countries. The partial computer output below shows the results from a two sample t-test. Which of the following below is true?
Birthweight boxplots labelled NK and SK. Vertical scale 0 to 12. NK has its median near 6, box from about 4.8 to 7, and whiskers from about 3.8 to 7.6. SK has its median near 7.5, box from about 7 to 7.9, and whiskers from about 5.1 to 9.8. These positions are approximate readings of the plotted scale. Open full-size image S0524 Two sample T for NK vs. SK
Group N Mean Standard Deviation S.E.Mean NK 24 6 1.1 .2 SK 23 7.4 1.2 .3
95% CI for μ N K − μ S K \mu\mathrm{NK}-\mu\mathrm{SK} μ NK − μ SK
Source gap (S0524): Source inconsistency: The output prints T=4.4399 with a negative interval for the NK minus SK difference. The captured signs and values are retained.
A. The mean weight of babies in North Korea is not significantly different from the mean weight of babies in South KoreaB. The mean weight of babies in North Korea is significantly different than the mean weight of babies in South Korea.C. The mean weight of babies in North Korea is significantly higher than the mean weight of babies in South Korea at the .1 level.D. The mean weight of babies in North Korea is significantly higher than the mean weight of babies in South Korea at the .05 level.E. The mean weight of babies in North Korea is significantly higher than the mean weight of babies in South Korea at the .01 level.
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12. Below are three histograms for the same random variable at different sizes, n. Which answer could have the appropriate sample sizes for the histograms I, II, and III respectively?
Three histograms in left-to-right order I, II, III, each with Frequency vertically and Sample Value horizontally. I is sparse with isolated small bars and uneven gaps; its frequency tick labels all visibly read 2.5. II is a smooth roughly bell-shaped histogram with a peak near 1700 and a frequency scale to 1800. III is an irregular mound of bars with a frequency scale to 16. The original horizontal scale labels are preserved in the image. Open full-size image S0525 A. 100, 10, 10000B. 10, 10000, 100C. 10000, 10, 100D. 10, 100, 10000E. 100, 10000, 10
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13. The mean is exactly one-half the distance between the first and third quartile for a probability distribution. Which of the following graphs could be the distribution?
Five frequency curves labelled A through E with Sample Value horizontal axes. A drops steeply from a high frequency at the left to a long low right tail. B rises to an early peak and slopes down into a right tail. C rises steeply at the right with a long low left tail. D decreases gradually from high at the left toward zero at the right. E is a roughly symmetric bell shape centered near 2.5. Original numeric axis labels remain visible. Open full-size image S0526 A. Figure (A)B. Figure (B)C. Figure (C)D. Figure (D)E. Figure (E)
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14. The ages of a random sample of 170 shoppers at a local outlet mall were collected. According to the boxplot below, what was the approximate median age?
Vertical boxplot on a scale from 0 to 100, marked every 10. The lower whisker is near 5, lower box edge near 16, median line near 28, upper box edge near 77, and upper whisker near 93. Positions are approximate readings of the drawn scale. Open full-size image S0527 A. 27B. 33C. 50D. 76E. 93
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15. A random sample of weights lifted by Division I weightlifters is collected. Another random sample of the same size is collected for Division II weightlifters. The boxplots for the amount of weight lifted by both random samples is displayed below. Which of the following statements is true?
Horizontal boxplots of weight lifted in lbs, axis ticks 0, 50, 100, 150, 200, 250. Division I has a box roughly 95 to 140, median near 122, whiskers near 60 and 190, and an outlier near 208. Division II has a box roughly 179 to 230, median near 198, and whiskers near 138 and beyond 250. These positions are approximate readings of the source drawing. Open full-size image S0528 A. The interquartile range of weight lifted is different for Division I versus Division II weightlifters.B. Division I weightlifters can on average lift more weight than Division II weightlifters.C. There are no Division I weightlifters who can lift more than the median Division II weightlifter.D. There are more outliers in the Division II weightlifter group.E. The median amount lifted for the Division I versus the Division II weightlifters is about the same.
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16. At Sunnyvale High School, Richard and Mary are comparing their teaching effectiveness for the yearly history state-wide exams. They randomly sample 50 test scores from Richard’s students and 50 test scores from Mary’s students. The stem and leaf plot below shows the results. What is, respectively, the difference between the proportion of Richard’s students and Mary’s students who score 80% or more on the test and the standard deviation of this difference?
Richard (leaves as shown) Stem Mary (leaves as shown) 1 2 3 3 6 5 1 1 1 1 2 2 3 4 5 6 7 8 9 6 1 2 3 6 6 7 8 9 1 2 4 6 9 7 1 2 4 6 9 1 2 3 4 4 5 6 8 8 1 2 2 2 2 3 4 4 5 6 7 7 8 8 8 9 1 1 2 3 5 6 7 7 8 8 8 9 9 9 1 1 1 2 3 5 5 6 7 8 8 9 0 0 0 0 0 10 0 0
Key: 6 ∣ 2 = 62 % 6|2=62\% 6∣2 = 62%
Source gap (S0529): Source inconsistency: The visible leaves do not provide 50 scores for each teacher as stated in the prompt. The complete visible leaf rows and the original stated sample sizes are retained; missing scores are not inferred.
A. 4% and 9.6%B. 8% and 9.6%C. 4% and 9.9%D. 8% and 9.9%E. 9.6% and 9.9%
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17. The two graphs below represent the probability distribution of the scores when Harry and Sally play a game. Their scores are independent of each other. If Y represents the sampling distribution of the sum of their scores, for what value will Y be the highest?
Two bar charts with Probability axes from 0 to 0.6 and scores 0 through 4. Sally's score 2 bar reaches 0.5 and bars for 0, 1, 3, 4 reach approximately 0.125. Harry's bars for 1, 2, 4 reach 0.25; bars for 0 and 3 reach approximately 0.125. Sally is orange and Harry purple. Open full-size image S0530 A. 2B. 3C. 4D. 5E. 8
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18. 1000 values are drawn from the normal distribution with mean 3 and standard deviation 1. Which of the five histograms below could be the histogram for this sampling distribution?
Five histograms A through E, all with frequency vertical axes. A is bell-shaped around 0 with sample values about −2.5 to 2.1. B is bell-shaped around 3 with values about 0.2 to 5.8. C is strongly right-skewed with values about 0.38 to 13.5. D is strongly right-skewed with values about 4.27 to 39.4. E is bell-shaped around 3 with a much wider axis, about −6.1 to 12.8. Original bars and numeric labels are preserved. Open full-size image S0531 A. Figure (A)B. Figure (B)C. Figure (C)D. Figure (D)E. Figure (E)
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19. Available data on the cost of dinner at a Thai restaurant for individual patrons shows these ranges. Which of the statements below is necessarily true?
A. Eighty percent spent under $42.77B. Seventy-five spent between $15.33 and $42.77C. Most of the patrons spent $22.15D. At least half spent less than $22.15E. Twenty-five percent spent under $15.33 and fifty percent spent more than $42.77
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20. A business organizes a carpool/vanpool program and surveyed all 505 employees to get data on current usage patterns to decide whether or not the program should be expanded. Below is a list of statements that apply to a randomly chosen employee. Which one is true?
Carpool to Work Location of Home: Within 10 miles 10–50 miles 50–80 miles Total Yes 10 50 35 95 No 300 100 10 410 Total 310 150 45 505
A. If a person carpools to work, he is not more likely to live 10–50 miles away than 10 miles awayB. If a person does not carpool, he is more likely to live 50–80 miles away than less than 10 miles awayC. A person is less likely to carpool if he lives within 10 miles than if he lives 50–80 miles awayD. Most commuters carpoolE. Most commuters live 50–80 miles away
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21. The distribution of time spent cooking Thanksgiving dinner is normal with a mean of 4 hours and a standard deviation of 75 minutes. Which of the following probabilities is represented by the shaded area in the figure below?
Normal curve with vertical guides. The shaded area runs from the guide labelled μ−2σ to the central guide labelled μ. The rest of the curve is unshaded. Open full-size image S0534 The source labels the two boundaries μ − 2 σ \mu-2\sigma μ − 2 σ μ \mu μ
A. The probability between 165 minutes and 240 minutesB. The probability between 90 minutes and 240 minutesC. The probability between 90 minutes and 390 minutesD. The probability between 165 minutes and 315 minutesE. The probability between 240 minutes and 390 minutes
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22. The least squares regression line is superimposed on five scatterplots below of a y response versus an x covariate. Which scatterplot shows a good fitting line to the data?
Five scatterplots labelled A through E, horizontal axes approximately 0 to 60 and vertical axes 2 to 8. A has a downward line through points spread on both sides across the x range. B has an upward line with most points concentrated below x=30. C has a downward line and many points clustered at small x below the line. D has a downward line with separate clusters around x=15–25 and x=35–50. E has a downward line with points concentrated at x=5–30. Original points and lines are preserved. Open full-size image S0535 A. Figure (A)B. Figure (B)C. Figure (C)D. Figure (D)E. Figure (E)
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23. Computer users were surveyed on the age of their computers. The following histogram describes the results of the survey. In which interval is the mean?
Histogram with Number of Customers vertical scale 0 to 140 in increments of 20 and Age of computer (years) horizontal categories. Approximate bar heights: 0–1 year 114; 1–2 years 80; 2–3 years 89; 3–4 years 40; Over 4 years 125. Values are approximate readings of the plotted scale; the last interval is open-ended. Open full-size image S0536 A. 0–1 yearB. 1–2 yearsC. 2–3 yearsD. Over 4 yearsE. Not enough information to know
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24. The ages of 220 seniors in a retirement home were recorded. What is an approximate first quartile of the ages from the boxplot below?
Vertical boxplot with Age axis marked from 40 to 120 in increments of 10. The lower box edge is near 78, median near 83, upper box edge near 103, lower whisker near 64, upper whisker near 114, and a low outlier near 60. Positions are approximate readings of the source scale. Open full-size image S0537 A. 25B. 61C. 78D. 83E. 103
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25. A suburb surveyed all residents to determine the proportion who work in government, academia, the non-profit sector, or business. Which statement is true?
A. The suburb would get more accurate information with a stratified random sampleB. The suburb can use this data to prove a causal link between residence in the suburb and work in the non-profit sectorC. The suburb would have to create a confidence interval to get an accurate estimate of the proportion of employees who work in businessD. Proportions determined using this data will be invalid because this was not a randomized study.E. Proportions determined using this data do not need confidence intervals constructed because this was a census
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26. The number of points obtainable in one round of a game is dependent on the number of points obtained in the previous round. In the first round, scores 0, 1, 2, and 3 can be chosen with equal probability. When the game is played twice, scores 0, 1, 2, and 3 are all available to be chosen again. However, the score chosen in round 1 is doubled and added to the pool of possible second round choices. Thus, in round 2 there are five possible choices of scores that can be chosen with equal probability. For example, if 1 is chosen in the first round, 2 is added to the pool of possible second round choices. 0, 1, 2, 2, and 3 can be chosen with equal probability in the second round. If Y represents the sampling distribution of the sum of scores when the game is played twice, for which value of Y will the probability be greatest?
A. 0B. 2C. 3D. 5E. 9
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27. A casino dealer flips a fair coin twenty times. She gets 8 heads and 12 tails. What is the probability of this outcome?
Source gap (S0539): Source ambiguity: The prompt does not distinguish 8 heads in any order from one fixed sequence of flips. Its count and probability expressions appear as separate choices, with no complete count-event expression shown. The original choices are retained without combining them or inferring the intended key.
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28. Alfredo is training for a 10 mile charity race. The probability that he wins first place is .15. The probability that Alfredo achieves his goal of running 10 miles in under an hour is .8. The probability that he both achieves his goal and wins first is .02. Given that he achieves his goal of running 10 miles in under an hour, what is the probability that he wins first place?
A. 0.8B. 0.02C. 0.15D. 0.133E. 0.025
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29. A university buys computers in bulk to get discounted rates. The probability distribution of X, the number of computers bought in a single order is shown in the table below. The cost per package is Y = 50 X − X 2 Y=50X-X^2 Y = 50 X − X 2
X = # of computers in the package 1 2 10 25 Probability .15 .25 .3 .3
Source gap (S0540): Source numerical inconsistency: The expected cost implied by the displayed distribution and formula does not match any listed price. The original table, formula, stated expected value of X, and choices are retained. No calculated cost is presented as a captured answer.
A. $49B. $96.125C. $300.525D. $433.175E. $625
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30. Y is a normally distributed random variable with a mean of 15 and a standard deviation of 1.5. X is a normally distributed random variable with a mean of 5 and a standard deviation of .3. Which of the below answers is equal to P ( X + Y > 21 ) P(X+Y>21) P ( X + Y > 21 )
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31. A simple random sample of 900 women has been used to create a confidence interval to estimate the mean number of pregnancies per woman. If the investigator decreases the sample size from 900 to 100, how will the width of the confidence interval change?
A. The width of the new interval will be about the sameB. The width of the new interval will be about 1/2 the size of the original intervalC. The width of the new interval will be about twice the size of the original intervalD. The width of the new interval will be about 1/3 the size of the original intervalE. The width of the new interval will be about three times the size of the original interval
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32. Assume the null hypothesis H 0 : μ = 5 H_0:\mu=5 H 0 : μ = 5
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33. Systolic blood pressure is considered high when it is above 35 mmHg. A random sample of a high risk group produces a mean of 41 mmHg. People in the group are weighing a medical intervention to reduce the group blood pressure. What is an appropriate alternative hypothesis for their concern?
Source gap (S0542): Source wording note: The threshold of 35 mmHg and sample mean of 41 mmHg are reproduced exactly from the practice question.
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34. An AP statistics student tests the difference between the proportion of AP and regular economics students who spend 4 hours or more studying the night before an economics exam. He randomly selects 10 AP students and 8 regular students. 30% of the advanced placement students spent 4 hours or more studying the night before the exam while 12.5% of the regular students spent 4 hours or more studying the night before the exam. He uses a large sample z-confidence interval to test the difference in proportions. Which of the following statements about the p-value obtained from the hypothesis test and the conclusion of the significance test is true?
A. The difference between 30% and 12.5% is large. Therefore there is a significant difference between the amount of the time the advanced placement and regular students spend studying.B. The p-value is less than .01. There is a significant difference between the two groups.C. The p-value is greater than .01 but less than .05. There is a significant difference between the two groups.D. The p-value is greater than .05 but less than .1. There is a significant difference between the two groups.E. The large sample approximation is not valid because np is too small.
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35. 70% of the respondents in a random sample of 2500 soda drinkers favor Brand A while 30% favor Brand B. What is the approximate margin of error for an 80% level of confidence for the percent of drinkers favoring Brand A?
A. .009%B. 1.285%C. 3.00%D. 1.118%E. 4.523%
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36. The 88% confidence interval for the proportion of car reservations that are no-shows is (.035, .078). What is the point estimate?
Source gap (S0544): Source numerical inconsistency: The midpoint of the displayed confidence interval is not among the listed point-estimate choices. The original interval and choices are retained without supplying a corrected option or inferring a key.
A. 0.033B. 0.0165C. 0.012D. 0.088E. 0.0515
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37. 70 customers out of 120 support new changes in an e-commerce company’s policy. A 99% confidence interval for the proportion in favor of the policy is.
Source gap (S0544): Source method and numerical uncertainty: The source does not specify a confidence-interval method. Its count, sample size, and confidence level do not produce any listed interval under the usual Normal approximation. The original values and choices are retained without attributing a method or answer key to the source.
A. (.59, .81)B. (.62, .78)C. (.63, .77)D. (.66, .74)E. (.23, .89)
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38. A director of a large start-up company is interested in the occupational choices of the former employees of that company, especially how many go on to work at two companies that she considers direct competition. She is able to collect data on 330 of the former employees, and this data is displayed in the table below. Which of the following statements is true?
Competitor A Competitor B Other Organization Retirement Total 1–5 years 25 25 45 25 120 1–5 years 10 20 20 50 100 20 or more years 5 10 5 90 110 Total 40 55 70 165 330
Source gap (S0545): Source inconsistency: Both of the first two row labels read “1–5 years” in the screenshot. The repeated label and all table entries are retained as shown.
A. Working for Competitor A is more likely than working for some other organization than Competitor BB. Working for Competitor A is more likely than working for Competitor BC. Retiring is more likely than working at Competitor AD. Those who work 1–5 years are more likely to retire than work for Competitor BE. Retiring is less likely than working at Competitor B
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39. In an Arizona zoo, all the female lions were examined to determine the percentage of pregnant lions. Analysis of the results will provide exact results for what population?
A. All female wild animals in the zoo.B. All female lions in Arizona.C. All female wild animals in Arizona.D. All female lions in the United StatesE. All female lions in the zoo.
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40. There are 50 classes in each of the grades at Jansen middle school. Grades 6–8 are represented at this middle school. Each class is assigned a homeroom number from 1 to 150. A random number generator is used to select 40 random numbers out of a list of numbers ordered from 1 to 150. These numbers are matched to the homeroom numbers and all the students in each selected class is surveyed. What type of study sample design is this?
A. stratified random sampleB. cluster random sampleC. simple random sampleD. censusE. nonrandom sample
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Source gap (S0546): The source ends this section with a “Check Answers” button. Its result is not captured, so the reconstructed choices do not grade or reveal a key.