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Stat 1430 SP23 Midterm
1. Bob wants to conduct a poll of 100 registered voters. He gets a list of registered voters and starts in a random spot, and begins calling people, going down the list. If someone does not answer he chooses the next name on the list and keeps going until he gets 100 people to answer the phone and answer his questions. It takes 150 names to complete his data set. Is this a random sample?
a. Yes b. No
2. Suppose you give 10 people a taste test where they each try samples of two different brands of soda. You randomize the order in which the soda samples are given to the participants. After drinking both samples they tell you which soda they liked best. What is a/the factor in this experiment?
a. number of subjects
b. brand of soda used
c. the order in which the samples were given to the subjects
d. which brand of soda each subject liked best
3. We know that if a histogram is skewed left, then the mean is less than the median. This is because:
a. There are a few small values in the data set compared to the rest.
b. There are a few large values in the data set compared to the rest.
4. Suppose at the end of the year everyone at Bob’s restaurant gets a 5 percent raise per hour to their existing wages. How does this raise affect the standard deviation of their wages?
a. standard deviation is larger than before
b. standard deviation is the same as before
c. standard deviation is smaller than before
5. A taxi cab company takes a random sample of 50 of its taxis and notes their miles per gallon (mpg) on a test run. The computer output is shown below.
|
Mean |
St Dev |
Min |
Q1 |
Median |
Q3 |
Max |
|
19.78 |
3.09 |
13.30 |
17.80 |
20.00 |
21.83 |
26.00 |
75% of the taxis have a MPG lower than what value?
a. 17.80
b. 21.83
c. 26 * .75 = 19.5
6. A taxi cab company takes a random sample of 50 of its taxis and notes their miles per gallon (MPG) on a test run. Which of the following descriptive statistics for their data is NOT in units of MPG?
a. IQR
b. Q1
c. All of these choices are in units of MPG
d. standard deviation
7. It is possible to have a data set with a correlation of positive 0.96, and have no points lying on the best-fitting line.
a. True
b. False
8. A data set contains the following 4 points: (1, 2) (2, 3) (3, 3) and (4, 5).
The value of SSE for this data set is 0. Hint: Draw a picture of the points
a. Yes
b. No
c. Not enough information to tell
9. We are comparing years of education and hours on the internet in the last month, to see if a relationship exists. If a relationship does exist, we want to predict Internet use using education level. The output is given below. Assume a scatterplot shows a linear pattern.
Variable Mean StDev Variance Minimum Maximum
Educatio 11.000 1.920 3.687 7.000 17.000
Internet 26.316 9.411 88.570 2.000 54.000
Pearson’s Correlation: 0.642
True or False? The slope of this regression line is 26.316.
a. True
b. False
10. Suppose we have two vaiables X and Y and we are using X to predict Y. Here is the regression analysis:
Predictor Coef SE Coef T P-value
Constant -90.88 52.62 -1.73 0.12
X 0.15556 0.0260 5.97 0.00
True or False: We know that the correlation coefficient r will be negative.
a. True
b. False
11. Suppose 5 students have the following scores, given as quiz 1 score, quiz 2 score:
Student 1: 10, 10
Student 2: 9, 8
Student 3: 6, 8
Student 4: 5, 9
Student 5: 8, 9
The regression analysis shows r = .76. The equation of the best fitting regression line is y = 4 + .5x where x = quiz 1 score (in points) and y = quiz 2 score (in points). Which student has the largest residual?
a. Student 1
b. Student 2
c. Student 3
d. Student 4
e. Student 5
12. An insurance company has collected the following data on the gender and marital status of 260 customers. Is there a relationship between gender and marital status?
|
Gender |
Married |
Not Married |
Total |
|
Male |
30 |
60 |
90 |
|
Female |
70 |
100 |
170 |
|
Total |
100 |
160 |
260 |
a. yes
b. no
13. An insurance company has collected the following data on the gender and marital status of 260 customers. What is the name for the following distribution? (Note the numbers sum to one, as they should.)
60/160
100/160
|
Gender |
Married |
Not Married |
Total |
|
Male |
30 |
60 |
90 |
|
Female |
50 |
100 |
150 |
|
Total |
80 |
160 |
240 |
a. conditional distribution of gender given not married
b. joint distribution of gender and not married
c. conditional distribution of not married given gender
d. marginal distribution of gender given not married
14. A(n) ______________________ probability is the probability of a single event occurring, with no regard to the other variable.
a. marginal
b. conditional
c. joint
d. None of the other choices is correct
15. Suppose you examine whether your 100 randomly chosen customers are male or female, and whether they made a purchase at your store. Your results are in the following table. Let M= male, F=female, P=purchase, and NP=no purchase. What does the number 17/100 represent?
|
|
Purchase |
No Purchase |
Total |
|
Male |
15 |
17 |
32 |
|
Female |
25 |
43 |
68 |
|
Total |
40 |
60 |
100 |
a. P(NP and M)
b. P(NP|M)
c. P(M|NP)
d. None of the other choices is correct
16. If P(A) = 0.35, P(B) = 0.45 and P(A and B) =0.25, then P(A|B) is:
a. .56
b. .40
c. .80
d. .71
17. Suppose 25% of students have an iPad. You take a random sample of 2 students. What is the chance that only one of them owns an iPad?
a. .25
b. .1875
c. .3750
d. None of the other choices is correct
18.
|
|
Short trip |
Long trip |
Total |
|
Forgets something important |
.20 |
.60 |
.80 |
|
Doesn't forget something important |
.05 |
.15 |
.20 |
|
Total |
.25 |
.75 |
1 |
Bob is planning a trip to visit his cousin in Chicago. We compare the length of his trip (short or long) to whether or not he’ll forget to pack something important. What can we tell from the probabilities in the table?
a. Bob forgets something important more often when he takes a short trip compared to a long trip.
b. Bob forgets something important less often when he takes a short trip compared to a long trip.
c. Bob forgets something important just as often when he’s on a short trip as he does on a long trip.
19. P(A|B) + P(A|NOT B) = 1
a. True
b. False
20. A survey asks 500 randomly selected U.S. taxpayers whether they have ever cheated on their taxes. Which of the following is an example of response bias in this situation?
a. Bob answers “no” even though he really has cheated on his taxes.
b. Bob was not selected to participate in the survey.
c. All of the these choices are examples of response bias.
d. Bob does not respond to the survey.
21. We know 50% of the data values always lie below the median. Is it also true that 50% of the data values always lie below the mean?
a. Yes b. No
22. Bob collects data on unemployment rates in all the counties in Ohio for 2019. He arranges his data in a relative frequency histogram. What is the label he should put on the Y axis?
a. % of counties
b. number of counties
c. rate of unemployment (%)
23. In a study of calories and sodium in hot dogs, a computer found the regression equation is Calories = 61.6 + 0.232 * Sodium (mg). How do we interpret the slope of this line?
a. As the amount of sodium increases by 1 milligram, the calories increase by 0.232
b. As the amount of sodium increases by 1 milligram, the calories increase by 61.6
c. As the amount of calories increases by 1, the sodium increases by 0.232 milligrams
d. As the amount of calories increases by 1, the sodium increases by 61.6 milligrams.
24. It is possible to find two different histograms whose data give you the same boxplot.
a. True
b. False
25. The coefficient of determination measures the percentage of points that lie directly on the regression line.
a. True
b. False