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AP Statistics – Chapter 11 & 12 – Hypothesis Testing – One Sample – Study Guide
1. An a statistical accurate experiment on side effects of pain relievers assigned arthritis patients to one of
several over-the-counter pain medications. Of the 440 patients who took one brand of pain reliever, 23
suffered some “adverse symptom.”
a. Does this experiment provide strong evidence that fewer than 10% of patients who take this
medication have adverse symptoms? Perform an appropriate test with α = .01.
b. Interpret the P-value in the context of the problem.
c. Describe a Type I error and a Type II error in this situation. What are the consequences of each?
d. Find and interpret a 99% confidence interval for the proportion of adverse symptoms for the overthe-counter pain medication.
e. If the evidence is statistically significant to support the pain medicine, is it practical to invest in it?
f. What does “99% confidence” mean?
2.
Non-exercise activity thermogenesis (NEAT) is energy burned by fidgeting, maintenance of posture,
spontaneous muscle contraction, and other activities of daily living. According to a previous study, 16
were randomly and independently sampled subjects increased their NEAT by 328 calories per day in
response to the additional food intake. The standard deviation from the sample was 256.
a. Test the null hypothesis that there was no change in NEAT versus the two-sided alternative. Assume
all the conditions for Hypothesis are satisfied.
b. Describe the types of errors you could make, and describe the consequences.
c. Calculate and interpret a 95% confidence interval for the change in NEAT.
3. The design of controls and instruments affects how easily people can use them. A student project
investigated this effect by asking 25 right-handed students to turn a knob (with their right hand) that
moved an indicator by screw action. There were two identical instruments, one with a right-hand (the
knob turns clockwise) and the other with a left-hand thread (the knob turns counterclockwise). The
following table gives the times in seconds each subject took to move the indicator a fixed distance.
a. Each of the 25 students used both instruments. Discuss briefly how you would use randomization in
arranging the experiment.
b. The project designers hoped to show that right-handed people find right-hand threads easier to use.
Carry out significance test at the 5% significance level to investigate this claim.
c. Describe a Type I and a Type II error in this situation, and give a possible consequence of each.
d. Given a mean difference of 5 seconds between the left-hand and right-hand times, interpret what
“the power of the test is 0.2703” means. Is this sufficient power?
Right
Left
Subject Thread Thread
1
113
137
2
105
105
3
130
133
4
101
108
5
138
115
6
118
170
7
87
103
8
116
145
9
75
78
10
96
107
11
122
84
12
103
148
13
116
147
Subject
14
15
16
17
18
19
20
21
22
23
24
25
Right
Thread
107
118
103
111
104
111
89
78
100
89
85
88
Left
Thread
87
166
146
123
135
112
93
76
116
78
102
123
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AP Statistics – Chapter 11 & 12 – Hypothesis Testing – One Sample – Study Guide – Answers
23
0.0523  01
.
 0.0523 , z 
 3.34 , Pvalue  0.0004
440
(.1)(.9)
440
1b. Assuming 10% of the patients suffered from adverse symptoms, the probability of a proportion being .0523
or less is 0.0004.
1c. Type I: The actual proportion of people who suffer from adverse symptoms is 0.1, but we concluded that it
was less. The doctors may prescribe it more, and more people may needlessly suffer. Type II: The actual
proportion of people who suffer from adverse symptoms is not 0.1, but we concluded that is. We say the
drug affects more people than what is actually true. The company may not sell it as well as they could. Type
I is more serious because the researchers do not want to mislead customers.
1d. I am 99% confident that the true population proportion for adverse symptoms for this medication is between
.025 and .08.
1e.The company should invest in the drug, because only about 3 to 8 percent of people suffer from it.
1f. If you were to continue to collect many, many sample and calculate many, many confidence intervals about
99% of the confidence intervals would contain the true population proportion of patients who suffer from
adverse symptoms.
1a. H0 : p  0.1 , H A : p  01
. , p 
328  0
 5125
. , df  15 , Pvalue  0.0012
256
16
2b. Type I: NEAT does not affect the burning of calories, but we concluded that it does. People will be acting
funny because they believe it will help to burn calories. Type II: NEAT does affect the burning of calories,
but we concluded that it does not. People could burn more calories by NEAT, but won’t try because they
believe it does not help.
2c. With t  2.131 , the 95% confidence interval is 191.6 to 464.4 cal/day. This tells us how much of the
additional calories might have been burned by the increase in NEAT: It consumed 19% to 46% of the extra
1000 cal/day.
2a. H0 :   0 , H A :   0 , t 
3a. Assign every individual a number 01-25. Use a random number table to select 12 (or13) of the individuals
to try the right thread first, while the other group would try the left thread first. After a break, switch threads
and repeat the experiment.
13.32  0
 2.9037 , df  24 , Pvalue  0.0039
3b. H0 :  R  L , H A :  R  L  0 , t 
22.936
25
Since 0.0039 is less than the significance level  .05 , we reject H 0 and conclude that there is statistically
significant evidence to support the hypothesis that right-handed people find right-hand threads easier to use.
3c. A Type I error is committed when the designers conclude that right-handed people find right-hand threads
easier to use when in fact there is no difference in the times. The consequence of this error is that the
designers would create two different instruments when it is unnecessary. A Type II error is committed when
the designers conclude that there is no difference in the times when in fact there is. The consequence of this
error is that designers will create one instrument when two are needed.
3d. If the true mean difference is 5 seconds (not equal to zero), then the probability of rejecting the null
hypotheses that there is not difference (mean = 0) is 0.2703. This is a very low power.