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you will receive the grade AB (Absent) for this exam.
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14 pages ( 83 problems ), 3 tables (Normal , t - Table and Chi-Square) at the end.
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Good luck and Happy Holidays!
Question 1-6 pertains to the histogram below.
Pretend the figure below is a histogram for the number of times students laughed out loud in Stat 100 class this semester.
Class intervals include the left-endpoint but not the right. (For example someone who laughed 10 times would fall in the 10- 20
block not the 5-10 block.) The height of each block is given in parentheses.
(6)
Number of times
1. 25 % of the students laughed 5 - 10 times. What percentage of the students laughed 20-30 times?
a) 10% b) 15% c) 20% d) 25% e) 30%
2. The median is closest to a) 5 b) 6 c) 9 d) 15 e) 20 3. The average is ___________the median a) less than b) greater than c) equal to d) cannot be determined 4. The 90 th percentile is a) 5 b) 20 c) 30 d) 40 e) 45 5. Did more people laugh 0-10 times or 20-50 times, or are they the same? a) 0- 10 b) 20- 50 c) Same 6. If everyone had laughed ten more times this semester, would the average, median and SD all increase by 10?
a. No, only the average would increase by 10. b. No, only the median would increase by 10. c. No, only the SD would increase by 10. d. No, the average and median would increase by 10, but the SD would stay the same. e. Yes, the average would increase by 10, the median would increase by 10 and SD would increase by 10.
For the next 4 questions match the scatter plots with their corresponding correlation coefficients
7 ) Correlation coefficient = - 0.94 a) Plot A b) Plot B c) Plot C d) Plot D
8 ) Correlation coefficient = - 0.75 a) Plot A b) Plot B c) Plot C d) Plot D
9 ) Correlation coefficient = 0. 57 a) Plot A b) Plot B c) Plot C d) Plot D
10 ) Correlation coefficient = 0. 03 a) Plot A b) Plot B c) Plot C d) Plot D
The next 3 questions pertain to the following experimental design:
A study was done to see if Orlistat, a drug that prevents absorption of fat from foods, could help obese people lose weight.
The subjects were 1000 obese adults who wanted to lose weight. Half were randomly selected to take Orlistat daily and half
were randomly selected to take a dummy pill daily. Neither the subjects nor those who evaluated their progress knew who was
in which group. The subjects were followed for 2 years. Both groups lost an average of 5 lbs.
19 ) Which of the following statements is best? (Answer this question based only on the information above, not on the chart below.)
a) This was a randomized controlled double-blind experiment. b) This was an observational study with controls and a placebo. c) This was a randomized controlled single-blind experiment.
Not everyone in the study took his or her medicine. Those who faithfully took their medicine were called “adherers” and those
who didn’t were called “non-adherers”. The adherers lost an average of 10 lbs. and the non-adherers lost an average of 0 lbs. as
shown in the table below:
Ave # of lbs. lost per person on Orlistat
Ave # of lbs. lost per person on Placebo
Adherers 10 lbs. 10 lbs.
Non-Adherers 0 lbs. 0 lbs.
Total 5 lbs. 5 lbs.
20 ) Since those who faithfully took Orlistat lost an average of 10 lbs. and those who neglected to take it didn’t lose anything, do
the results from the table above show that Orlistat works better than a placebo? a) Yes ` b) No
21 ) Which one of the following could best explain why the adherers lost more weight that the non-adherers?
a) Those who took Orlistat lost more weight because the Orlistat prevented the absorption of fats from the foods they ate. b) Adherers are different than non-adherers; the adherers were more responsible about taking their medicine and so may also be more responsible about their health in general (for example, they may have a healthier diet and exercise more regularly.) c) Orlistat cannot work if you don’t take it. Non-adherers didn’t lose any weight because they didn’t take Orlistat.
The next 3 questions pertain to the 3 histograms below representing 3 variables from the 530 responses to
Survey 1: height in inches, number of shoes owned by females in this class, and number of times you ever
cheated on an exam. Below each histogram are 2 numbers, one is the average and the other is the median.
Histogram A Histogram B Histogram C
22 ) Which histogram represents height? a) Histogram A b) Histogram B c) Histogram C
23 ) Which histogram represents shoes? a) Histogram A b) Histogram B c) Histogram C
24 ) What is the average number of times people in our class said they had ever cheated on an exam?
a) 3 b) 7.69433 c) 18 d) 20.5511 e) 66.
The next 8 questions pertain to the height and weight data collected from the 530 responses to Survey 1 this semester.
The 5 summary statistics and the scatter plot are shown below:
25. Two lines are shown. One is the regression and one is the SD line. Which is the regression line? a) Line A b) Line B
26. Which line is the point of averages on? a) Regression Line only b ) SD line only c) Both d) Neither
27 ) If everyone in the class gained 10 lbs …. (Assume the heights remain the same)
a) Both the SD and the correlation coefficient would increase
b) Both the SD and the correlation coefficient would stay the same.
c) The correlation coefficient would increase but the SD would remain the same.
d) The SD would increase but the correlation coefficient would remain the same.
28 ) Suppose the 530 heights and weights were converted from inches and pounds to centimeters and kilograms. Would the
correlation coefficient change?
a) Yes b) No c) cannot be determined from the information given
29 ) One student is 2 SD’s above average in height. What is the regression estimate for how many SD’s above average he is in
weight?
a) 2 b) 1.3 c) 1 d) 0
30 ) Student X and Student Y are both 62.5” tall. Student X lies on the regression line and Student Y lies on the SD line.
How much do they each weigh? a) X weighs 146 and Y weighs 114 lbs.
b) X weighs 114 lbs and Y weighs 146 lbs.
c) X weighs 125.2 and Y weighs 114 lbs.
d) X weighs 114 lbs. and Y weighs 125.2 lbs.
31 ) What is the slope of the regression line for predicting weight from height?
a) 0.65* 32 lbs./4” b) 0.65 c) 0.65 * 4”/32 lbs.
32 ) The RMSE for predicting weights from heights is
a)
2 1! 0. 65 * 4” b)
2 1! 0. 65 * 32 lbs. c)
2 1! 0. 5 * 4”. d)
2 1! 0. 5 * 32 lbs.
Average SD Height 66. 5 ” 4” Weight 146 lbs. 32 lbs.
Correlation: r = 0.
The next 4 questions pertain to the following situation:
A recent ABC news poll, asked a simple random sample of 1015 adults nationwide: "Do you think grade-school teachers should or should not be permitted to spank children at school?" 26% answered that they should be able to spank children.
42. What most closely resembles the relevant box model?
a) It has 1015 tickets, 26% are marked "1" and 74% are marked "0"
b) It has 1015 tickets with an average of 0.
c) It has millions of tickets marked "0" and "1", but the exact percentage of each is unknown.
43. The draws are made ___________replacement. a) With b) Without
44. The SE of the sample percent is about 1.38% An approximate 95% confidence interval for the percentage of all Americans who think grade school teachers should be able to spank children at school is
a) (23.24%-28.76%) b) (24.62%-27.38%) c) (22%-30%)
45. If the researcher increased his sample size by a factor of 4 (to n = 4060) then the length of the 95% confidence interval would a) increase by a factor of 2 b) increase by a factor of 4 c) decrease by a factor of 2 d) decrease by a factor of 4
The next 5 questions pertain to the following situation:
A husband and wife claim that they have a special bond that allows them to communicate by ESP. To test this claim an investigator puts the husband and wife in separate rooms. The husband is asked 100 true/false questions and after each question he is given 5 seconds to use his ESP to try to communicate his answer to his wife. His wife has no idea what the questions are and cannot see or hear him. She writes down what she thinks he communicated to her by ESP. She correctly identifies 60 of rof
her husband’s 100 answers. The null hypothesis is that she just guessed her husband’s answers.
46 ) Which of the following most accurately describes the null box?
a) It has 100 tickets, 60 marked "1" and 40 marked "0" b) It has 100 tickets, 50 marked "1" and 50 marked "-1" c) It has 2 tickets, 1 marked "1" and 1 marked "0"
47 ) The draws are made _________ replacement. a) with b) without
48 ) Assuming the null hypothesis to be true, we would expect the wife to correctly guess 50 of her husband’s answers give or take _______questions. Fill in the blank with the correct SE.
a) 5 b) 0.5 c) 10 d) 2
49 ) The z - statistic for testing whether the hypothesis is true is
a) 10 /SD of the box b) 10 / SE for the sum c) 10 /SE for percent d) 10 /SE for the average
50 ) What can you conclude? a) Reject the null and conclude that there’s strong evidence that the wife is not just guessing
b) Reject the null and conclude that there’s strong evidence that the wife is just guessing.
c) Reject the null and conclude that the wife must have ESP.
The next 3 questions pertain to the following situation:
A gambler was watching a dice game and noticed that one of the dice seemed to come up with a " 3 " more often than it should.
He grabbed the die and rolled it 60 times. He got a " 3 " 15 times. The null hypothesis is that the die is fair.
51 ) Which of the following most accurately describes the null box?
a) It has 6 tickets, one marked " 3 " and five marked "0" b) It has 6 tickets, one each of "1", "2", "3", "4", "5", "6". c) It has 6 tickets, one marked “1” and five marked “0” d) It has 60 tickets, 15 marked “3” and 45 marked “0”
52 ) The z-statistic for testing whether the null hypothesis is true is closest to
a) 60 * 1 / 6 * 5 / 6
5 b) 1 / 6 * 5 / 6
5 c) 1 /^6 *****^5 /^660 d) 60 * 1 / 6 * 5 / 6
53 ) The P-value is about 1% so the appropriate conclusion is …
a) To accept the null hypothesis b) To reject the null hypothesis c) That it is plausible to think that the excess “3”s could be due to chance.
The next 2 questions pertain to a large group of people whose IQ scores are normally distributed with an
average = 100 and an SD= 15
54. What percent of the people have IQ scores under 70?
a) 16% b) 5% c) 2.5% d) 1%
55. What IQ score corresponds to the 84 th percentile? (In other words, what IQ score is higher than 84% of the scores.)
a) 100 b) 115 c) 84 d) 112 e) cannot be determined
The next question pertains to this situation:
Suppose a large group of husbands and wives are given personality tests measuring their aggression level, and the
correlation between the scores of the husbands and the scores of the wives is negative 0.5 (supporting the theory that
opposites attract).
56. If a husband scores in the 90 th percentile, the regression estimate for his wife’s percentile on the test is closest to
a) 90
th b) 75
th c) 50
th d) 26
th e) 10
th
The next 3 questions pertain to the following poll:
An ABC News Poll conducted in October 2005 asked 400 men and 4 00 women the following question:
“Would you personally like to live to be 120 years old if medical breakthroughs made that possible?” Only 33 % of
women said “Yes”, compared with 49 % of men. The null hypothesis is that this 16 % difference is due to chance.
57. Which of the following most accurately describes the null box(es)?
a. There is one null box with 1000 tickets marked with "0"s and "1"s. b. There are 2 null boxes, each with 500 tickets marked with "0"s and "1"s. c. There are 2 null boxes, each with millions of tickets. The 2 boxes have the same percentage of "1"s and "0"s d. There are 2 null boxes, each with millions of tickets. One box has 71% "1"s, and the other has 63% "1"s.
58. The draws are made ________replacement. a) with b) without
59. The SE for the men’s and women’s sample percentages are both about 2.5%. The SE for the difference of the 2 sample
percentages is closest to …
a) 0 % b) 2.5% c) 3.5% d) 5 % e) 10 %
The next 6 questions pertain to the following situation: A large lecture course has 4 00 students, broken down into small discussion sections led by teaching assistants. On the final, the class average is 75. However, in one section of 16 students, the average is 80 with a SD of 10. The TA of that section wonders whether this difference reflects something real (like his teaching skills) or could it simply be due to chance variation. He would like to do a significance test.
68. The TA knows that the scores of the class are normally distributed but does not know the SD of the class; he only knows the SD of his section. What test statistic should he use? a. The t-statistic b. The z - statistic c. Neither without knowing the SD of the class.
69. The TA decides to compute both statistics (and decide later which he should use). If he does his calculations correctly which statistic would be bigger? a. The t-statistic b. The z- statistic c. Not enough information to determine
70. If he uses the t-statistic he would estimate the SD of the large lecture to be
a) 10 b) 16 / 15 *10 c) 15 / 16 *10 d) 10/
71. Using the t-test, how many degrees of freedom would there be? a. 10 b. 12 c. 15. d. 16 e. 80
7 2. The t-statistic is 1.94, so the P-value is a. between 5% and 10% b. between 2.5% and 5% c. less than 1%
73. If the TA also knew, in addition to the information given above, that the SD of the large lecture was 12, then which test statistic should he now use? a. t-statistic b. z-statistic c. chi-square statistic
The next 4 questions pertain to the following hypothetical survey: Suppose a random sample of 60 female and 40 male Stat 100 students were asked the question: “Which one of the following do you think would most improve Stat 100: food, movies, gambling?” The results are shown in the table below. Course Improvements Food Movies Gambling Total Female 30 20 10 60 Male 20 10 10 40
74. To test the null hypothesis that there is no real difference in course improvement preferences between Stat 100 males and females you would use a a. one sample z test b. 2 sample z test c. t-test d. chi-square test for goodness-of-fit e. chi-square test for independence
75. How many degrees of freedom are there? a) 1 b) 2 c) 3 d) 4 e) 5
76. Assuming the null hypothesis is true, what is the expected number of females who would choose gambling as the best improvement? a) 6 b) 8 c) 10 d) 12 e) 15
77. The test statistic is 1.39, what do you conclude?
a) Reject the null because P < 5% b) Reject the null because P> 5% c) Cannot reject the null, it looks like male and female choices are not very different for this question.
The next 4 questions pertain to the following situation:
Suppose a huge statistics class of 1500 students has the final grade distribution displayed in the table below. Now suppose a group of 100 students are chosen from the 1500 to participate in a focus group about the course. The number of students who received each grade is also shown in the table. The question is: were the students randomly selected?
Grade Huge Class Group of 100 chosen from class A 3 0% 50 B 40 % 40 C 20 % 5 D and lower 10% 5 Total 100% 100
78. To test the null hypothesis that the focus group was selected as a simple random sample you would use a) one sample z test b) 2 sample z test c) t test d) chi-square test for goodness-of-fit e) chi-square test for independence
79. The test statistic is closest to
a) 13.3 b) 27 c) 11.25 d) 15
80. The number of degrees of freedom is
a) 1 b) 2 c) 3 d) 4 e) 5
81. What do you conclude?
a) Reject the null, extremely strong evidence that the focus group was not randomly selected. b) It’s quite plausible that the focus group was randomly selected.
Questions 82 - 83 82 ) Which of the following does a test of significance deal with?
a) Is the difference important? b) What caused the difference? c) Was the experiment properly designed? d) Is the difference due to chance? e) All of the above
83 ) Suppose an investigator tests 1000 couples who all claim to have ESP by running the same experiment 100 times (one spouse in each couple would try to “divine” the other spouses answers on the 100 question true/false exam). Suppose none of the couples really have ESP and the experiments are done correctly. Would you expect the investigator to find statistically significant evidence of ESP for any of the couples? (That is, would you expect a P value of 5% or less for any of the couples?)
a) Yes, one could expect statistically significant evidence for about 50 of the 10 00 couples even if none of them had ESP b) Yes, one could expect statistically significant evidence for about 5 of the 1000 couples even if none of them had ESP c) No, if the experiments were done correctly they would confirm that none of the people have ESP.
Question 84 If you could choose whatever grade you’d like for this course, which grade would you choose?
t
STUDENT’S t - TABLE Degrees of freedom 25% 10% 5% 2.5% 1% 0.5% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Student’s curve, with degrees of freedom shown at the left of the table The shaded area is shown along the top of the table Is shown in the
