Statistics Class Level Test Mu Alpha Theta State 2008

Transcription

1 Statistics Class Level Test Mu Alpha Theta State Which of the following are true statements? I. The histogram of a binomial distribution with p = 0.5 is always symmetric no matter what n, the number of trials, is. II. The histogram of a binomial distribution with p = 0.9 and n = 7 is skewed to the right. III. The histogram of a binomial distribution with p = 0.9 is almost symmetric if n is very large. (A) I and II (B) I and III (C) II and III (D) I, II, and III 2. The type of sampling in which each member of the population selected for the sample is returned to the population before the next member is selected is called (A) Sampling without replacement (B) Sampling with replacement (C) Simple random sampling (D) Systematic sampling 3. The summary statistics for selling prices (in thousands of dollars) of 35 luxury condominiums are as follows: x Sx Min. Q1 Med. Q3 Max Which of the following correctly determines the boundaries for outliers in this distribution? (A) 545 ±1.5 (460) (B) (510) and (510) (C) 651 ± 1.5 (510) (D) (460) and (460) 4. The Academic Registrar compiled data on 11,000 students, which were summarized in a contingency table. The survey results were cross-classified by gender and department of study. GENDER Science Humanities Business Arts Total Male (M) Female (F) Total Suppose a student is randomly selected. What is the probability (to the nearest thousandth) that a student is either a male or in the Humanities department? (A) (B) (C) (D) A politician wants to know what percentage of the voters supports her position on the issue of forced busing for integration. What size voter sample should be obtained to determine with 90% confidence the support level to within 4%? (A) 21 (B) 25 (C) 423 (D) 600

2 6. We wish to investigate if a new medicine is effective in reducing the length and severity of the flu. We take the next 20 patients that come to the walk-in clinic complaining of flu and, after a medical exam to verify that the patients do have the flu, we give them the new medicine and tell them about the new drug we are giving them. One week later, the patients are contacted and 15 patients state the new remedy was helpful in reducing the severity and length of the illness. Which of the following is NOT CORRECT? (A) This is a poor experiment because there is no control group. We do not know how many would feel better in a week without treatment. (B) This is a poor experiment because it is not double-blinded. The patients may feel relief because they thought the drug should work. (C) This is a poor experiment because a convenience sample was selected. Patients who come to the walk-in clinic may have more severe flu than people who do not. (D) This is a poor experiment because we didn t give the remedy to people without the flu to assess its effect in a control group. 7. The marketing manager of a pharmaceutical company believes that more girls than boys use its acne medicine. In a recent survey, 2500 teenagers are asked whether or not they use that particular product. The responses, separated by sex, are summarized below. Use acne Total medicine Female Male Give a 90% confidence interval for the difference between the proportion of girls and boys who use this acne medication. (A) ± ( 1.4 ) ( 1.34 ) ± 1.96 (B).4 ( 1.4 ) ( 1.34) 1150 ( ).4.34 ± (C) ( ).4.34 ± (D) According to a CBS/New York Times poll taken in 1992, 15% of the public have responded to a telephone call-in poll. In a random group of five people, what is the probability (to the nearest thousandth) that exactly two have responded to a call-in poll? (A).138 (B).165 (C).300 (D).835

3 9. Lice are a pesky problem for school aged children and is unrelated to cleanliness. The lifetimes of lice that have fallen off the scalp onto bedding is approximately normally distributed with a mean of 2.2 days and a standard deviation of 0.4 days. We would expect that once the lice start falling off the scalp, 90% of the lice would die within days (to the nearest tenth): (A) 2.6 days (B) 3.9 days (C) 2.5 days (D) 2.7 days 10. Which of the following statements is correct? I. You can reduce the probability of a Type I error by decreasing your value for α. II. You can reduce the probability of a Type II error by increasing your sample size. III. If you reduce the probability of a Type I error, you automatically reduce the probability of a Type II error as well. (A) II only (B) I and II. (C) II and III. (D) I, II, and III. 11. The average length of stay in a hospital is useful for planning purposes. Suppose that the following is the distribution of the length of stay in a hospital after a minor operation: Days Prob The average length of stay is: (A) 4.2 days (B).17 days (C) 3.3 days (D) 4.0 days 12. The Correcto Publishing Company claims that its publications will have errors only twice in every 100 pages. What is the approximate probability that Anne will read 235 pages of a 790-page book published by Correcto before finding an error? (A) 0.02% (B) 2% (C) 5% (D) 16% 13. Suppose that the distribution of math SAT scores from your state this year is normally distributed with mean 480 and standard deviation 100 for males, and mean 440 and standard deviation 120 for females. If someone who scores 780 or higher on math SAT can be considered a genius, what is the approximate proportion of geniuses among the male SAT takers? (A) 28% (B) 15% (C) 3% (D) 1.5%

4 14. Seventeen people have been exposed to a particular disease. Each one independently has a 40% chance of contracting the disease. A hospital has the capacity to handle 10 cases of the disease. What is the probability (to the nearest thousandth) that the hospital s capacity will be exceeded? (A) (B) (C) (D) Suppose that the scatterplot of log Y on X produces a correlation close to 1. Which of the following is true? I. The correlation between the variables X and Y may also have a correlation close to 1. II. The residual plot of Y on X will show a clearly curved pattern of points. III. The difference between consecutive values of y for equal x-intervals is approximately constant. (A) I and II only (B) I and III only (C) II and III only (D) I, II, and III 16. A researcher wishes to compare the effects of 2 fertilizers on the yield of a soybean crop. She has 20 plots of land available and she decides to use a paired experiment using 10 pairs of plots. Thus, she will: (A) use a table of random numbers to divide the 20 plots into 10 pairs and then, for each pair, flip a coin to assign the fertilizers to the 2 plots. (B) subjectively divide the 20 plots into 10 pairs (making the plots within a block as similar as possible) and then, for each pair, flip a coin to assign the fertilizers to the 2 plots. (C) use a table of random numbers to divide the 20 plots into 10 pairs and then use the table of random numbers a second time to decide upon the fertilizer to be applied to each pair. (D) flip a coin to divide the 20 plots into 10 pairs and then, for each pair, use a table of random numbers to assign the fertilizers to the 2 plots. 17. A publisher uses standard boxes for shipping books. The mean weight of books packed per box is 25 pounds, with a standard deviation of 2 pounds. The mean weight of the boxes is 1 pound, with a standard deviation of 0.15 pounds. The mean weight of the packing material used per box is 2 pounds, with a standard deviation of 0.25 pounds. What is the standard deviation (to the nearest thousandth) of the weights of the packed boxes? (A) pounds (B) pounds (C) pounds (D) pounds 18. A study was conducted to estimate the effectiveness of doing assignments in an introductory statistics course. Students in one section taught by instructor A received assignments. Students in another section taught by instructor B, received no assignments. The final grade of each student was recorded. A 95% confidence interval for the difference in the mean grades (Section A - Section B) was computed to be 3.5 ± 1.8. This means: (A) There is evidence that doing assignments improves the average grade because the difference in the population means is negative. (B) There is little evidence that doing assignments improves the average grade because the 95% confidence interval does not cover 0. (C) There is evidence that doing assignments improves the average grade because the 95% confidence is entirely positive. (D) There is evidence that doing assignments does not improve the average grade because the 95% confidence interval does not cover 0.

5 19. Suppose the regression equation for predicting success on a dexterity task (y) from number of training sessions (x) is y = x and s y s x = What percentage of the variation in y is NOT explained by the regression on x? (A) 81% (B) 19% (C) 66% (D) 34% 20. Seven sets of identical twins are given psychological tests to determine whether the firstborn of the twins tends to be more aggressive than the second born. The results are shown in the following table, where the higher score represents greater aggressiveness. Set Firstborn Second born Difference If we are willing to assume that the necessary conditions for inference hold true, then the approximate value of the appropriate test statistic is: (A) and we would reject H0 at α =.05 (B) 1.71 and we would reject H0 at α =.05 (C) 1.71 and we would not reject H0 at α =.05 (D) and we would not reject H0 at α = The following numbers are extracted from a table of random digits: A scientist will be measuring the total amount of mercury content in a random sample of sites selected without replacement from a population of 75 sites. The sites are labeled 01, 02,..., 75 and she starts at the beginning of the line of random digits and takes consecutive pairs of digits. Which of the following is correct? (A) Her sample is 81, 15, 50, 02, 27 (B) Her sample is 81, 50, 27, 93, 82 (C) Her sample is 50, 27, 24, 09, 41 (D) Her sample is 50, 27, 24, 09, An experiment was designed to investigate the effect of the amount of water and seed variety upon subsequent growth of plants. Each plant was potted in a randomly selected clay plot, and a measured amount of water was given weekly. The height of the plant at the end of the experiment was measured. Which of the following is NOT correct? (A) The response variable is the plant height. (B) The explanatory variables are the amount of water and seed variety. (C) Randomization was used to even out the effect of other possible factors upon the growth of the plants. (D) The researcher should vary the amount of water each seed gets so that each seed gets treated with every amount of water.

6 23. In a survey or airline travelers, subjects were observed in the coach section of airplanes to determine if men or women are bothered by a seatmate of the opposite gender using the common armrest. ( Passengers who were asleep or lovers cuddled together were not counted, since these were considered confounding circumstances. ) BOTHERED NOT BOTHERED Females Males What is the probability that a randomly chosen passenger is bothered? is bothered, given that the passenger is male? (A) 19/45; 38/56 (B) 57/101; 38/101 (C) 38/56; 38/101 (D) 57/101;38/57 What is the probability that a randomly selected passenger 24. Refer to the previous problem. Are the events being male and being bothered independent? (A) No, because P(bothered) P(bothered Male) (B) Yes, because P(bothered) = P(bothered Male) (C) No, because P(bothered) = P(bothered Male) (D) Yes, because P(bothered) P(bothered Male) 25. Twenty types of beef hot dogs were tested for calories and sodium (mg). The hot dogs averaged calories with a standard deviation of 22.64, and the sodium level averaged mg with a standard deviation of mg. The correlation was given as r = To the nearest hundredth, the equation of the least-squares regression line (LSRL) predicting sodium level from number of calories is (A) y = x (B) y = x (C) y = x (D) y = x 26. Two 90% confidence interval estimates are obtained: I (28.5, 34.5) and II ( ). a. If the sample sizes are the same, which has the larger standard deviation? b. If the sample standard deviations are the same, which has the larger size? (A) a. I b. I (B) a. I b. II (C) a. II b. I (D) a. II b. II 27. Which of the following lead to binomial distributions? I. An inspection procedure at an automobile manufacturing plant involves selecting a sample of 20 cars from the assembly line and noting for each whether there are no defects, at least one major defect, or only minor defects. II. As students study more and more during their AP Statistics class, their chances of getting an A on any given test continue to improve. The teacher is interested in the probability of any given student receiving various numbers of A s on the 8 class exams. III. A committee of two is to be selected from among the five teachers and ten students attending a meeting. What are the probabilities that the committee will consist of two teachers, of two students, or of exactly one teacher and one student? (A) I only (B) II only (C) III only (D) II and III

7 28. In a certain community, 20% of cable subscribers also subscribe to the company's broadband service for their Internet connection. You would like to design a simulation to estimate the probability that one of six randomly selected subscribers has the broadband service. Using digits 0 through 9, which of the following assignments would be appropriate to model this situation? (A) Assign even digits to broadband subscribers and odd digits to cable-only subscribers. (B) Assign 0 and 1 to broadband subscribers and 2,3,4,5,6,7,8, and 9 to cable-only subscribers. (C) Assign 0,1, and 2 to broadband subscribers and 3, 4, 5, 6, 7, 8, and 9 to cable-only subscribers. (D) Assign 0, 1, and 2 to broadband subscribers; 3,4,5, and 6 to cable only subscribers; and ignore digits 7, 8, and An analyst, using a random sample of n = 500 families, obtained a 90 percent confidence interval for mean monthly family income for a large population: ($600, $800). If the analyst had used a 99 percent confidence coefficient instead, the confidence interval would be: (A) narrower and less likely to contain the population mean family income (B) wider and more likely to contain the population mean family income (C) narrower and more likely to contain the population mean family income (D) wider and less likely to contain the population mean family income 30. A state auditor is given an assignment to choose and audit 26 companies. She lists all companies whose name begins with A, assigns each a number, and uses a random number table to pick one of these numbers and thus one company. She proceeds to use the same procedure for each letter of the alphabet and then combines the 26 results into a group for auditing. Which of the following are true statements? I. Her procedure makes use of chance. II. Her procedure results in a systematic random sample. III. Each company has an equal probability of being audited. (A) I and II (B) I and III (C) II and III (D) I, II, and III 31. The Barbarian Aptitude Test (BAT) gives each Barbarian two scores, one for pillaging and one for burning. The scores range from a low of 0 to a high of 50. The least squares equation for a large group of Barbarians who took the BAT is Predicted Burning = Pillaging Which of the following is the best interpretation of the slope of this line? (A) Barbarians tend to score about 0.3 point higher on burning than on pillaging. (B) Barbarians score about 30% as many points on burning as on pillaging. (C) The burning score is highly correlated with the pillaging score. (D) A Barbarian who earned 1 more point on pillaging than another Barbarian tended to earn only 0.3 point more on burning. 32. For the sake of efficiency, a shoe company decides to produce the left shoe of each pair at one site and the right shoe at a different site. If the two sites produce shoes with a number of defects reflected by µ1= 0.002, σ1= 0.15 and µ2 = 0.005, σ2 = 0.18, what is the mean and standard deviation for the number of defects for pairs of shoes produced by this company? (A) µ = , σ= (B) µ = , σ= (C) µ = 0.007, σ= (D) µ = 0.007, σ =

8 33. In a game of chance, three fair coins are tossed simultaneously. If all three coins show heads, then the player wins $15. If all three coins show tails, then the player wins $10. Any other flips result in $0 won. If it costs $5 to play the game, what is the player's expected net gain or loss at the end of two games? (A) The player can expect to lose $3.75 after two games. (B) The player can expect to gain $1.88 after two games. (C) The player can expect to gain $3.75 after two games. (D) The player can expect to lose $1.88 after two games. 34. A recent estimate by a large distributor of gasoline claims that 60% of all cars stopping at their service stations chose unleaded gas and that super unleaded and regular were each selected 20% of the time. In order to check the validity of these proportions, a study was conducted of cars stopping at the distributor's service stations in a large city. The results were as follows: Gasoline Selected Regular Unleaded Super Unleaded The value of the appropriate test statistic and approximate p-value, respectively, are: (A) 13.15,.0014 (B) (C) 13.15,.0028 (D) 13.15, The effects of a toxic pollutant upon fish were examined by placing fish in a two liter solution of water with various concentrations of the pollutant. The researchers wanted to see if there was any type of association between the level or pollutant and the time it took for the fish to show distress. The time (in minutes) until the fish showed distress was recorded at which time the fish were removed from the container. A total of 18 pairs of data were collected. Note that the pollutant is measured on a logarithmic scale where a change of one unit represents an increase of 10 fold in the pollution concentration. A preliminary plot of the data showed that the relationship of time vs. log(pollution) was approximately linear. The computer output appears at the top of the next column. T FOR H0: PARAMETER=0 PARAMETER ESTIMATE STD ERROR OF ESTIMATE TEST STAT PR > T INTERCEPT LOGPOLLUT A 95% confidence interval for the slope is: (A) 7.56 ± 1.96(1.978) (B) ± 1.96(0.438) (C) 7.56 ± 2.12(1.978) (D) ± 2.12 (.438) 36. The average yearly snowfall in Chillyville is normally distributed with a mean of 55 inches. If the snowfall in Chillyville exceeds 60 inches in 15% of the years, what is the standard deviation (to the nearest hundredth)? (A) 0.21 inches (B) 4.82 inches (C) 5.18 inches (D) 5.00 inches

9 37. Consumer Reports found that Duracell Alkaline AA batteries have a mean lifetime of 4.1 hours and a standard deviation of 1.8 hours. Eveready Energizer AA batteries have a mean lifetime of 4.5 hours with a standard deviation of 2.0 hours. Assume both battery lifetimes are normally distributed. If you choose one of each battery at random, then to the nearest thousandth what is the probability that the Duracell lasts longer than the Eveready? (A) (B) (C) (D) A basketball player with a poor foul-shot record practices intensively during the off-season. He tells the coach that he has raised his proficiency from 60% to 90%. Dubious, the coach asks him to take 10 shots, and will only be convinced that the player has improved if he hits 90% or more. Find the probability to the nearest thousandth of a Type I error occurring. (A) (B) (C) (D) A researcher who wanted to estimate the mean batting average of baseball players decided to take a sample of 25 professional baseball players and record their batting average. His confidence interval for the true mean batting average of all baseball players was ( , ). Determine what level of significance the researcher used. Assume that batting averages have a standard deviation of σ = (A) 74% (B) 87% (C) 94% (D) 97% 40. A company plans to sell a new product at $60 per unit. Variable costs per unit may be $20 (with a probability of 0.4) or $12. Fixed costs per week are $2000 and demand per week may be 200 units (probability 0.75) or 400 units. What is the expected weekly profit assuming that production is adjusted to demand? (A) $3800 (B) $9200 (C)$7200 (D) $15000

10 Answers: 1. B 2. B 3. D 4. A 5. C 6. D 7. E 8. A 9. D 10. B 11. E 12. A 13. E 14. A 15. A 16. B 17. D 18. C 19. D 20. C 21. C 22. D 23. E 24. A 25. A 26. C 27. E 28. B 29. B 30. E 31. D 32. D 33. A 34. A 35. D 36. B 37. A 38. C 39. C 40. B