Download Short Answer Exam Review

Short Answer Exam Review
STA 2023
Short Answer
Assume that a simple random sample has been selected from a normally distributed population and test
the given claim. Use either the traditional method or P-value method. Identify the null hypothesis and
alternative hypothesis, test statistic, critical values(s) or P-value, conclusion about the null hypothesis,
and the final conclusion that addreses the original claim.
1. The mean resting pulse rate for men is 72 beats per minute. A simple random sample of men who regularly
work out at Mitch’s Gym is obtained and their resting pulse rates (in beats per minute) are listed below. Use a
0.05 significance level to test the claim that these sample pulse rates come from a population with a mean less
than 72 beats per minute. Assume that the standard deviation of the resting pulse rates of all men who work out
at Mitch’s Gym is unknown.
54
60
67
84
74
64
69
70
66
80
59
71
76
63
2. In a clinical study of an allergy drug, 108 of the 202 subjects reported experiencing significant relief from their
symptoms. At the 0.01 significance level, test the claim that more than half of all those using the drug
experience relief.
For 3 and 4, Construct the given Confidence Interval
3. A Gallop poll consisted of 1012 randomly selected adults who were asked whether “cloning of humans should
or should not be allowed.” Results showed that 901 adults surveyed indicated that cloning should not be
allowed. Construct a 95% confidence interval estimate of the proportion of adults believing that cloning of
humans should not be allowed.
4. Listed below are weights (in pounds) of glass discarded in one week by randomly selected households (based on
data from the Garbage Project at the University of Arizona):
3.52
8.87
3.99
3.61
2.33
3.21
0.25
4.94
Construct a 95% confidence interval estimate of the mean weight of glass discarded by all households
5. Sample data were obtained for the amount of rainfall (in inches) and the yield of bushels of oats per acre for a
selected sample. The equation of the regression line is
, where x represents the amount of
rainfall. Predict the yield when there are 5 inches of rain. Assume that there is a significant linear correlation
between the amount of rainfall and the yield.
6. Listed below are combined city-highway fuel economy ratings (in mi/gal) for different cars. The old ratings
are based on tests used before 2008 and the new ratings are based on tests that went into effect in 2008. Find an
equation for the regression line. Let x represent the old fuel economy ratings and y represent the new fuel
economy ratings.
Old
New
16
15
27
24
17
15
33
29
28
25
24
22
18
16
22
20
20
18
29
26
21
19
7. A flashlight has six batteries, two of which are defective. If two are selected at random without replacement,
find the probability that one is defective.
8. The probability of winning in a random drawing is .025. If you buy four tickets, what is the probability that
you will not win any prizes.
9. The following sorted values are the numbers of points scored in the Super Bowl for a recent period of 24 years.
Find the mean, median , midrange, range and standard deviation.
36
37
56
37
56
37
57
39
59
41
61
43
61
44
65
44
69
47
75
50
53
54
55
10. Scores on the SAT test have a mean of 1518 and a standard deviation of 325. Scores on the ACT test have a
mean of 21.1 and a standard deviatin of 4.8. Which is relatively better: a score of 1190 on the SAT test or a
score of 16.0 on the ACT test? Why?
Use the following table to answer questions 11,12 and 13.
cola
under 21 years of age 20
between 21 and 40
20
over 40 years of age 35
root beer
35
40
20
lemon-lime
30
30
25
11. If one of the 255 subjects is randomly selected, find the probability that the person is between 21 and 40 and
drink lemon-lime.
12. If one of the 255 subjects is randomly selected, find the probability that the person is under 21 or drinks root
beer.
13. If one of the 255 subjects is randomly selected, find the probability that the person drinks cola given that he/she
is over 40.
Short Answer Exam Review
STA 2023
Answer Section
SHORT ANSWER
1.
2.
72 beats per minute.
72 beats per minute. Test statistic: t = -1.639.
critical t value = 1.771. Fail to reject the null hypothesis. There is not sufficient evidence to support the
claim that the sample pulse rates came from a population with a mean less than 72 beats per minute.
.
. Test statistic: z = 0.99. P- value: p = 0.1623. Fail to reject the null hypothesis.
There is not sufficient evidence to support the claim that more than half of all those using the drug experience
relief.
0.871 < p < 0.910
1.786 lb < µ < 5.894 lb
41.7 bushels
3.
4.
5.
6.
7. 8/15
8. .9037
9. mean: 51.13
median: 53
midrange: 55.5
range: 39
standard deviation: 11.10
10. The score of 1190 converts to z = -1.01, and the score of 16.0 converts to z = -1.06, so the score of 1190 is
relatively better because it has the larger z score.
11. 0.1176
12. 0.5686
13. 0.4375