STAT 1342 - Exam One
(Test Form A)
1-3. Consider a sample of 26 guinea pigs. We counted the pigs in six weight ranges and
record them in the following table.
Weight
counts
range
0.91-1.00kg
5
1.01-1.10kg
12
1.11-1.20kg
5
1.21-1.30kg
2
1.31-1.40kg
1
1.41-1.50kg
1
1. The sample mode weight is in the category of____kg.
(a)1.01-1.10
(b) 1.11-1.20
(c) 1.21-1.30
(d) none of above
Highest frequency is between 1.01-1.10.
2. If the heaviest guinea pig were recorded as 2.00 kg by mistake instead of the
correct weight, the mode weight would be greater.
(a) True
(b) False
If the weight of the heaviest pig is corrected then also the mode of the data will
be same, because the mode lies between 1.01-1.10Kg.
3. Suppose that the Q1=1.03 kg and Q3=1.17 kg, about what percent of pigs are
weighed between 1.03kg and 1.17 kg? (5 points)
(a) 75 %
(b) 68%
(c) 50%
(d) 25%
We know, between Q1 and Q3 there are 50% of the observations.
4-5. For a Physics course containing 10 students, the maximum point total for the
quarter was 200. The point totals for the 10 students are given in the following stem
plot.
Stem
Leaf
11
7 8
12
1 4 8
13
0 7
14
2 6
15
16
17
8
4. For the above number set calculate the five number summary
Min, Q1, Median, Q2, Maximum
(a) 116, 121 , 129, 142, 179
(b) 117, 121, 129, 142, 178
(c) 116, 121, 133.50, 142, 179
(d)117, 120.25, 133.50, 143.5, 178
1
5. This distribution of sample scores is best described as ________.
(a) symmetric about its mean
(b) skewed to the right
(c) skewed to the left
(d) None of above
The rate at which the frequency increased is more than the rate at which the
frequency decreased. This is evident from the stem-leaf plot.
6. To rate TV shows, phone surveys are sometimes used. Such a survey might
record several variables, some of which are listed below. Which of these
variables is categorical?
(a) the number of persons watching the show
(b) the ages of all persons watching the show
(c) the number of times the show has been watched in the last month
(d) the name of the show (if any) being watched
Categorical or qualitative variable, is basically the odd-man-out problem.
7. A survey is conducted on students taking a statistics class. Several variables
are measured in the survey. Which of these variables listed below is
quantitative?
(a) the number of credit hours taken during the quarter
(b) the gender
(c) the parents name
(d) the state of the High School
Quantitative variable, again is a odd-man-out problem.
8-10. Scores on a University exam have a mean of 80 and a standard deviation of 7.
8. Atleast what percentage of students have scores between 66 and 94?
(a) 68%
(b) 75%
(c) 95%
(d) 90%
Chebyshev’s rule, because we don’t know anything about the distribution of
data.
9. If the distribution of data is symmetric, about 95% data will fall within what two
values?
(a) (73, 87)
(b) (60,100) (c) (66,94) (d) (68,95)
Emperical rule, because we know that the distribution of data is symmetric.
10. If the distribution of data is symmetric, about what percent of data will be
between 2 standard deviations from the mean.
(a) 68%
(b) 75%
(c) 95%
(d) 90%
Emperical rule: Between mean -2*SD and mean + 2*SD we can get 95% of the
observations.
2
11-12. Consider the following scatterplot of the weight of several models of cars (in
pounds) vs. their horsepower.
300
Horsepower
250
200
150
100
50
2000
2500
3000
Weight
3500
4000
4500
11. A plausible value for the correlation between weight and mpg is
(a) -0.8
(b) -0.1 (c) +0.1 (d) +0.8
12. Correlation between height and weight will be decreased if we measure the
weight using kilograms instead of pounds.
(a)True
(b) False
Correlation is unitless.
13-18. We want to investigate if the average age at which infants begin to crawl (y) can
be predicted from the average outdoor temperature (x) six months after birth when
they are likely to begin crawling. We decide to fit a least-squares regression line to
the data with x as the explanatory variable and y as the response variable. We
compute the following quantities.
r = correlation between x and y = 0.9
x = mean of the values of x = 55.85
y = mean of the values of y = 30.25
sx = standard deviation of the values of x = 15.25
sy = standard deviation of the values of y = 2.78
13-18 Use of formulas (see my notes titled Regression)
13. The slope of the least-squares line is?
(a) 0.16
(b) -.99
(c) 0.11
(d) 4.13
14. Y-intercept of the least squares line is?
(a) 21.09
(b) 24.67
(c) 36.83
(d) 51.87
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15. Equation of the line is?
(a) Y=36.83-0.11X
(b) Y=21.09-0.16X
(c) Y=36.83+4.1X
(d) Y=21.09+0.16X
16. Predict crawl age at room temperature of 50oC?
(a) 12.38
(b) 29.09
(c) 8.32
(d) 11.33
17. Suppose the crawl age at room temperature of 50oC is 28, then, calculate the
residual.
(a) 3.33 (b) -3.33
(c) 1.09
(d) -1.09
18. What is the coefficient of determination?
(a) 90% (b) 81%
(c) 1.09
(d) none of above
19-20. There are 4 red balls and 6 green balls in a jar. You draw two balls without
replacement.
19. What is the probability of drawing a red ball then a green ball?
4 6
4 6
46
46


(a)
(b)
(c)
(d)
10 9
10 10
10
9
20. What is the probability of drawing a red and a green ball (in any order)?
4 6 4 6
4 6 6 4
 + 
  
(a)
(b)
10 10 10 9
10 9 10 9
46 46
4 6
6 4

  
(c)
(d)
9
10
10 10 10 10
Please look at my notes titled “Probability-2”.
21-22. (Q. 22 is a bonus question and contains 5 points)
All human blood can be typed as one of O, A, B, or AB. The distribution of the types
varies a bit with race. Choose a black American at random. Here are the
approximate probabilities that the person you choose will have blood type O, B, or
AB.
Blood Type
O
A
B
AB
Probability
0.40
?
0.32
0.08
21. The probability that the person chosen has a blood type other than O is
(a) 0.3
(b) 0.6
(c) 0.5
(d) 0.4
Here you need to find the probability of the compliment of an event.
P( choosing a person with blood type O) = 0.4
So, P( choosing a person with blood type other than O) = 1 - 0.4 = 0.6
4
22. An a group of 2 randomly chosen students, what is the probability that none of them
is Type O blood
(a) 0.6×0.6
(b) 0.6×0.4
(c) 0.4×0.4
(d) None of these
Hints: This problem is similar to drawing marbles with replacement.
So, required probability =
= P (First person don’t have blood type O) × P(Second person don’t have blood type O)
23-26.
Diagnostic tests of medical conditions can have several types of results. Test results
can be either positive (TR+) or negative (TR-). A TR+ indicates that the patient has the
condition and TR- indicates that the patient does not have the consition. (Note: A TR+
does not PROVE that the patient has the condition.
To understand the effectiveness of the diagnostic test 200 persons were selected.
Based on this answer the following:
CP: The condition is present
CA: The condition is absent
CP
CA
Total
TR+
100
30
130
TR-
20
50
70
Total
120
80
200
For a person selected at random, compute:
23. P(TR+|CP)
(a) 100/200
(b) 100/130
(c) 100/120
(d) 30/80
24.P(TR+|CA)
(a) 100/200
(b) 30/130
(c) 100/120
(d) 30/80
25.P(TR-|CP)
(a) 20/120
(b) 20/70
(c) 50/80
26. P(CP)
(a) 20/120
(b) 30/130
(c) 120/200
(d) 50/70
(d) 80/200
Similar (only numbers changed) to Question 26, chapter 5 (page 203).
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