obs
gpa
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
13.00
14.00
15.00
16.00
17.00
18.00
19.00
20.00
21.00
22.00
23.00
24.00
25.00
26.00
27.00
28.00
29.00
30.00
31.00
32.00
33.00
34.00
35.00
36.00
37.00
38.00
39.00
40.00
41.00
42.00
43.00
44.00
45.00
46.00
hsm
3.32
2.26
2.35
2.08
3.38
3.29
3.21
2.00
3.18
2.34
3.08
3.34
1.40
1.43
2.48
3.73
3.80
4.00
2.00
3.74
2.32
2.79
3.21
3.08
3.75
3.16
2.73
3.06
1.07
3.35
1.82
3.12
2.25
2.93
3.16
2.83
3.10
3.07
2.87
3.61
2.17
1.95
3.35
3.58
2.75
3.26
hss
10.00
6.00
8.00
9.00
8.00
10.00
8.00
3.00
9.00
7.00
9.00
5.00
6.00
10.00
8.00
10.00
10.00
9.00
9.00
9.00
9.00
8.00
7.00
9.00
10.00
10.00
9.00
8.00
7.00
10.00
6.00
10.00
9.00
10.00
9.00
10.00
9.00
7.00
9.00
10.00
10.00
7.00
10.00
10.00
10.00
10.00
hse
10.00
8.00
6.00
10.00
9.00
8.00
8.00
7.00
10.00
7.00
10.00
9.00
8.00
9.00
9.00
10.00
10.00
9.00
6.00
10.00
7.00
8.00
9.00
10.00
9.00
9.00
8.00
10.00
8.00
10.00
8.00
10.00
7.00
10.00
7.00
9.00
10.00
4.00
9.00
10.00
7.00
8.00
10.00
7.00
7.00
10.00
10.00
5.00
8.00
7.00
8.00
8.00
7.00
6.00
8.00
6.00
6.00
7.00
8.00
9.00
6.00
9.00
9.00
8.00
5.00
9.00
8.00
7.00
8.00
8.00
9.00
8.00
7.00
10.00
6.00
10.00
6.00
7.00
4.00
10.00
7.00
9.00
9.00
7.00
9.00
9.00
7.00
9.00
10.00
8.00
5.00
9.00
satm
satv
sex
670.00
600.00
700.00
640.00
640.00
530.00
670.00
600.00
540.00
580.00
760.00
630.00
600.00
400.00
460.00
530.00
670.00
450.00
570.00
480.00
491.00
488.00
600.00
600.00
510.00
530.00
750.00
610.00
650.00
460.00
720.00
630.00
760.00
500.00
800.00
610.00
640.00
670.00
750.00
700.00
520.00
440.00
610.00
530.00
505.00
435.00
559.00
607.00
760.00
620.00
640.00
490.00
520.00
360.00
580.00
460.00
700.00
520.00
620.00
570.00
490.00
550.00
640.00
520.00
550.00
290.00
600.00
520.00
400.00
390.00
710.00
530.00
750.00
670.00
660.00
480.00
620.00
480.00
630.00
440.00
650.00
450.00
550.00
570.00
730.00
650.00
710.00
400.00
770.00
720.00
610.00
560.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
47.00
48.00
49.00
50.00
51.00
52.00
53.00
54.00
55.00
56.00
57.00
58.00
59.00
60.00
61.00
62.00
63.00
64.00
65.00
66.00
67.00
68.00
69.00
70.00
71.00
72.00
73.00
74.00
75.00
76.00
77.00
78.00
79.00
80.00
81.00
82.00
83.00
84.00
85.00
86.00
87.00
88.00
89.00
90.00
91.00
92.00
93.00
3.41
3.67
3.81
3.30
2.30
3.62
3.20
2.55
2.82
3.25
2.21
2.50
3.03
1.92
4.00
1.81
2.70
2.96
2.76
2.71
3.40
2.65
2.48
3.86
2.62
3.72
3.50
2.83
3.06
4.00
3.70
2.81
1.93
3.70
2.96
2.64
3.09
3.00
2.97
2.81
3.32
3.40
1.84
0.40
2.88
2.77
2.26
9.00
10.00
10.00
10.00
9.00
10.00
9.00
7.00
10.00
9.00
7.00
10.00
8.00
9.00
7.00
9.00
6.00
9.00
10.00
8.00
9.00
8.00
8.00
10.00
9.00
7.00
8.00
6.00
8.00
9.00
8.00
9.00
8.00
10.00
9.00
9.00
10.00
4.00
10.00
10.00
10.00
7.00
9.00
6.00
9.00
6.00
5.00
4.00
10.00
10.00
10.00
10.00
10.00
5.00
8.00
9.00
7.00
7.00
9.00
8.00
10.00
6.00
9.00
8.00
7.00
10.00
7.00
10.00
10.00
8.00
10.00
8.00
8.00
7.00
7.00
6.00
10.00
10.00
7.00
6.00
10.00
7.00
9.00
10.00
3.00
10.00
10.00
9.00
8.00
6.00
6.00
7.00
5.00
7.00
7.00
10.00
7.00
9.00
10.00
8.00
7.00
8.00
9.00
8.00
8.00
9.00
7.00
8.00
6.00
9.00
6.00
8.00
10.00
9.00
9.00
8.00
7.00
10.00
7.00
7.00
8.00
7.00
5.00
10.00
8.00
4.00
8.00
10.00
6.00
8.00
8.00
4.00
10.00
10.00
10.00
4.00
6.00
7.00
6.00
9.00
7.00
600.00
640.00
750.00
650.00
590.00
660.00
570.00
570.00
660.00
690.00
670.00
660.00
600.00
447.00
600.00
620.00
580.00
630.00
600.00
700.00
550.00
680.00
630.00
750.00
491.00
550.00
630.00
690.00
540.00
640.00
520.00
559.00
590.00
580.00
670.00
620.00
540.00
620.00
770.00
620.00
660.00
710.00
610.00
560.00
690.00
590.00
530.00
360.00
570.00
540.00
480.00
420.00
630.00
570.00
480.00
550.00
550.00
500.00
460.00
630.00
320.00
410.00
580.00
470.00
630.00
560.00
440.00
560.00
450.00
500.00
760.00
391.00
500.00
500.00
440.00
400.00
480.00
410.00
488.00
510.00
580.00
440.00
590.00
470.00
560.00
540.00
570.00
560.00
500.00
390.00
690.00
460.00
440.00
440.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
94.00
95.00
96.00
97.00
98.00
99.00
100.00
101.00
102.00
103.00
104.00
105.00
106.00
107.00
108.00
109.00
110.00
111.00
112.00
113.00
114.00
115.00
116.00
117.00
118.00
119.00
120.00
121.00
122.00
123.00
124.00
125.00
126.00
127.00
128.00
129.00
130.00
131.00
132.00
133.00
134.00
135.00
136.00
137.00
138.00
139.00
140.00
2.03
2.43
2.63
1.66
3.41
2.12
3.33
1.69
2.46
1.59
1.14
0.65
2.12
2.82
2.34
2.11
1.34
2.53
2.75
3.14
2.25
1.00
2.79
2.39
2.15
0.75
3.06
2.50
2.78
2.44
1.11
3.12
2.17
0.12
2.00
3.22
1.88
2.04
2.58
2.16
2.50
1.85
1.46
2.95
0.80
0.91
2.67
6.00
7.00
10.00
8.00
9.00
7.00
7.00
8.00
6.00
8.00
10.00
9.00
7.00
4.00
8.00
6.00
6.00
8.00
10.00
9.00
10.00
8.00
9.00
6.00
6.00
7.00
5.00
9.00
9.00
8.00
7.00
10.00
8.00
4.00
6.00
9.00
10.00
8.00
10.00
6.00
7.00
10.00
7.00
9.00
8.00
6.00
9.00
7.00
10.00
10.00
4.00
9.00
7.00
6.00
7.00
7.00
9.00
10.00
7.00
6.00
5.00
9.00
9.00
7.00
9.00
10.00
8.00
10.00
9.00
6.00
5.00
6.00
6.00
9.00
9.00
9.00
8.00
7.00
10.00
7.00
6.00
5.00
7.00
6.00
7.00
9.00
6.00
10.00
8.00
7.00
9.00
10.00
5.00
9.00
9.00
10.00
6.00
3.00
9.00
8.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
7.00
9.00
8.00
8.00
10.00
9.00
10.00
10.00
7.00
6.00
6.00
6.00
9.00
9.00
10.00
8.00
7.00
10.00
8.00
6.00
6.00
9.00
6.00
7.00
9.00
6.00
10.00
7.00
8.00
8.00
9.00
7.00
10.00
540.00
530.00
640.00
590.00
520.00
559.00
500.00
490.00
490.00
670.00
720.00
640.00
520.00
400.00
480.00
480.00
530.00
550.00
720.00
640.00
690.00
640.00
690.00
470.00
480.00
540.00
510.00
560.00
600.00
690.00
590.00
580.00
650.00
630.00
530.00
650.00
620.00
690.00
720.00
590.00
630.00
700.00
630.00
620.00
470.00
586.00
586.00
610.00
560.00
500.00
470.00
490.00
545.00
460.00
390.00
370.00
480.00
610.00
520.00
380.00
470.00
410.00
390.00
470.00
500.00
500.00
630.00
580.00
600.00
400.00
330.00
460.00
590.00
380.00
500.00
510.00
490.00
480.00
340.00
500.00
490.00
320.00
490.00
430.00
440.00
740.00
440.00
500.00
480.00
540.00
400.00
410.00
697.00
670.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
141.00
142.00
143.00
144.00
145.00
146.00
147.00
148.00
149.00
150.00
151.00
152.00
153.00
154.00
155.00
156.00
157.00
158.00
159.00
160.00
161.00
162.00
163.00
164.00
165.00
166.00
167.00
168.00
169.00
170.00
171.00
172.00
173.00
174.00
175.00
176.00
177.00
178.00
179.00
180.00
181.00
182.00
183.00
184.00
185.00
186.00
187.00
2.51
1.79
2.42
0.58
3.00
2.76
3.35
3.80
2.38
2.58
3.18
2.87
3.16
3.07
3.68
3.34
1.93
2.43
3.28
3.66
2.29
2.19
3.06
3.41
3.14
2.85
3.47
3.44
3.90
3.65
1.32
3.23
2.86
2.51
2.86
3.34
3.33
3.69
1.80
2.57
2.28
1.60
2.00
1.69
3.06
2.75
2.62
9.00
7.00
6.00
5.00
10.00
10.00
9.00
10.00
9.00
10.00
10.00
8.00
8.00
9.00
10.00
10.00
10.00
9.00
10.00
10.00
7.00
6.00
10.00
8.00
9.00
10.00
10.00
10.00
10.00
9.00
9.00
10.00
10.00
8.00
8.00
10.00
9.00
10.00
7.00
9.00
8.00
4.00
2.00
7.00
9.00
8.00
9.00
8.00
7.00
6.00
7.00
10.00
10.00
9.00
9.00
9.00
10.00
10.00
8.00
9.00
8.00
8.00
9.00
8.00
5.00
10.00
10.00
6.00
5.00
10.00
6.00
9.00
8.00
10.00
10.00
10.00
9.00
8.00
10.00
9.00
9.00
9.00
9.00
7.00
10.00
7.00
10.00
10.00
7.00
4.00
6.00
10.00
9.00
10.00
7.00
5.00
8.00
7.00
9.00
10.00
9.00
8.00
10.00
9.00
10.00
7.00
8.00
9.00
9.00
10.00
8.00
9.00
10.00
10.00
8.00
6.00
10.00
8.00
10.00
8.00
9.00
9.00
10.00
9.00
9.00
10.00
10.00
10.00
8.00
9.00
9.00
8.00
7.00
10.00
10.00
7.00
6.00
7.00
9.00
8.00
8.00
700.00
550.00
505.00
515.00
774.00
570.00
580.00
560.00
650.00
440.00
570.00
476.00
680.00
490.00
590.00
590.00
650.00
480.00
670.00
710.00
570.00
540.00
620.00
630.00
630.00
610.00
720.00
640.00
650.00
640.00
740.00
600.00
650.00
510.00
550.00
570.00
630.00
710.00
620.00
417.00
600.00
460.00
300.00
560.00
590.00
559.00
550.00
500.00
570.00
518.00
285.00
688.00
570.00
540.00
530.00
570.00
430.00
750.00
576.00
700.00
480.00
490.00
580.00
490.00
520.00
490.00
600.00
570.00
460.00
510.00
470.00
700.00
460.00
680.00
590.00
500.00
430.00
460.00
660.00
430.00
440.00
510.00
530.00
560.00
470.00
470.00
518.00
600.00
460.00
290.00
480.00
420.00
435.00
440.00
1.00
1.00
1.00
1.00
1.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
188.00
189.00
190.00
191.00
192.00
193.00
194.00
195.00
196.00
197.00
198.00
199.00
200.00
201.00
202.00
203.00
204.00
205.00
206.00
207.00
208.00
209.00
210.00
211.00
212.00
213.00
214.00
215.00
216.00
217.00
218.00
219.00
220.00
221.00
222.00
223.00
224.00
0.39
2.44
3.46
2.37
1.25
2.80
2.14
2.45
2.71
2.59
2.93
2.53
1.95
3.39
2.69
1.94
3.00
2.09
1.85
3.34
2.25
4.00
2.72
2.61
2.32
3.39
3.64
1.80
1.52
3.40
2.86
3.32
2.07
0.85
1.86
2.59
2.28
7.00
10.00
9.00
8.00
7.00
10.00
5.00
7.00
9.00
10.00
9.00
7.00
6.00
9.00
8.00
8.00
10.00
9.00
10.00
10.00
6.00
10.00
6.00
9.00
6.00
10.00
8.00
8.00
9.00
6.00
9.00
10.00
9.00
7.00
7.00
5.00
9.00
10.00
9.00
9.00
7.00
8.00
9.00
4.00
7.00
7.00
10.00
9.00
6.00
6.00
9.00
6.00
8.00
8.00
7.00
8.00
9.00
9.00
10.00
5.00
7.00
6.00
10.00
6.00
7.00
9.00
9.00
4.00
9.00
7.00
7.00
9.00
4.00
8.00
9.00
9.00
8.00
9.00
6.00
9.00
8.00
8.00
10.00
10.00
10.00
9.00
9.00
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9.00
8.00
9.00
8.00
10.00
10.00
10.00
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7.00
8.00
7.00
10.00
8.00
9.00
10.00
9.00
8.00
10.00
6.00
9.00
7.00
7.00
9.00
550.00
650.00
610.00
530.00
480.00
550.00
560.00
430.00
490.00
590.00
690.00
570.00
550.00
510.00
470.00
470.00
510.00
450.00
530.00
490.00
530.00
580.00
580.00
620.00
430.00
500.00
590.00
620.00
520.00
480.00
640.00
640.00
600.00
510.00
356.00
630.00
559.00
660.00
350.00
520.00
480.00
360.00
450.00
420.00
330.00
400.00
470.00
510.00
480.00
600.00
570.00
420.00
330.00
360.00
460.00
550.00
410.00
510.00
490.00
490.00
420.00
460.00
390.00
580.00
600.00
570.00
480.00
470.00
560.00
440.00
480.00
350.00
470.00
488.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
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2.00
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2.00
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2.00
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2.00
2.00
2.00
2.00
2.00
Williams 1
Briana Williams
Prof. Budnick
PSY 259 - 03
November 5, 2018
22. Calculating z Scores Using Excel
1. Open the data file CSdata.xlxs (*attachment*) in Excel. Plot a histogram of math SAT
scores of the students in this file (satm).
2. Convert every score in the distribution (math SAT) to a z score with Excel.
a. Using Excel, make a histogram of the new zsatm variable. What does it look like
(what is the shape)? How does it compare to the original satm histogram?
b. What is the mean and standard deviation? Explain why we get these values for the
mean and standard deviation. (Think about the z score formula.)
Using Standard Scores to Compare Different Distributions
Consider the following two standardized distributions:
●
3. Suppose that you got a 540 on the SAT and a 20 on the ACT for the distributions
described above. Which score is better?
●
4. Suppose that you got a 600 on the SAT and a 24 on the ACT. Which score is better?
23. The Normal Distribution
1. Answer the following questions about the normal distribution:
a. What percentage of the area under the curve is between the mean and the
rightmost end of the curve?
b. What percentage of the area under the curve is within one standard deviation of
the mean (on either side of the mean)?
2. Using the Unit Normal Table, determine the following:
a. Find the probabilities that correspond to the following z scores: 2.0, 0.5,
−0.75, −2.0
b. Find the z scores that correspond to the following probabilities: 0.5000, 0.8413,
0.3050
3. Assume that the following is true: The scale for the SAT is set so that the distribution of
scores is approximately normal with mean = 500 and standard deviation = 100.
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a.
b.
c.
d.
What is the probability of having an SAT score of 130 or above?
What is the probability of having an SAT score of 120 or above?
What is the probability of having an SAT score of 91 or less?
You think that you might need a tutor. You know of a tutoring service for students
who score between 350 and 650 on the SAT. You think that you probably fit
within their range. What is the probability that you will get an SAT score between
350 and 650?
e. The National Collegiate Athletic Association (NCAA) requires Division I athletes
to score at least 820 on the combined mathematics and verbal parts of the SAT
exam in order to compete in their first college year. In 1999, the scores of the
millions of students taking the SATs were approximately normal with a mean =
1017 and a standard deviation = 209. What is the probability of scoring an 820 or
less in this distribution?
24. z Scores and the Normal Distribution
Use the following means and standard deviations: for ACT, μ = 21, σ = 3 and for SAT, μ = 500,
σ = 100.
1. You take the ACT test and the SAT test. You get a 24 on the ACT and a 660 on the SAT.
The college that you apply to only needs one score. Which do you want to send them
(that is, which score is better: 24 or 660?). Why?
2. What is the probability of having an ACT score of 20 or less?
3. What SAT score do you need to have to be in the top 15% of the population?
4. What is the probability of scoring between 500 and 650 on the SAT?
5. What is your percentile rank if you have an ACT of 25.5?
25. Hypothesis Testing With Normal Populations
1. Each of the following situations calls for a significance test of a population mean. State
the null hypothesis H0 and the alternative hypothesis Ha in each case.
a. The diameter of a spindle in a small motor is supposed to be 5mm. If the spindle
is either too small or too large, the motor will not work properly. The
manufacturer measures the diameter in a sample of motors to determine whether
the mean diameter has moved away from the target.
b. Census Bureau data show that the mean household income in the area served by a
shopping mall is $52,500 per year. A market research firm questions shoppers at
the mall. The researchers suspect the mean household income of mall shoppers is
higher than that of the general population.
c. The examinations in a large psychology class are scaled after grading so that the
mean score is 50. The professor thinks that one teaching assistant is a poor teacher
and suspects that his students have a lower mean than the class as a whole. The
teaching assistant’s students this semester can be considered a sample from the
population of all students in the course, so the professor compares their mean
score with 50.
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2. A researcher would like to test the effectiveness of a newly developed growth hormone.
The researcher knows that under normal circumstances, laboratory rats reach an average
weight of 1,000 grams at 10 weeks of age. When the sample of 10 rats is weighed at 10
weeks, they weigh 1,010 grams.
a. Assuming that the growth hormone has no effect, what would a Type I error be in
this situation?
b. Assuming that the growth hormone does have an effect, what would a Type II
error be in this situation?
26. Stating Hypotheses and Choosing Tests
For each of the following scenarios, identify
a. whether a one-tailed test can be used or if a two-tailed test is more appropriate (remember
to use a one-tailed whenever you can find a directional alternative hypothesis to increase
power).
b. the null and alternative hypotheses.
c. the appropriate statistical test.
1. People with agoraphobia are so filled with anxiety about being in public places
that they seldom leave their homes. Knowing this is a difficult disorder to treat, a
researcher tries a long-term treatment. A sample of individuals reports how often
they have ventured out of the house in the past month. Then they receive
relaxation training and are introduced to trips away from the house at gradually
increasing durations. After two months of treatment, subjects report the number of
trips out of the house they made in the last 30 days. The researcher wants to
determine if the number of trips out of the house has increased after the treatment.
2. An experiment studied the effect of diet on blood pressure. Researchers randomly
divided 54 healthy adults into two groups. One group received a calcium
supplement. The other received a placebo. Blood pressure was measured at the
end of one month.
3. Suppose that during interpersonal social interactions (e.g., during business
meetings or talking to casual acquaintances), people in the United States maintain
an average distance of μ = 7 feet from other people. The distribution of distance
scores is normal with a σ = 1.5 feet. A researcher examines how people in the
United States compare in social interaction distance to social interaction distance
for people in Italy. A random sample of 40 Italians is observed during
interpersonal interactions. For this sample, the mean interaction distance is 4.5
feet. Do the Italians have closer social interactions than Americans do?
4. The animal learning course in a university’s psychology department requires that
each student train a rat to perform certain behaviors. The student’s grade is
partially determined by the rat’s performance. The instructor for the course has
noticed that some students are very comfortable working with the rats and seem to
be very successful training their rats. The instructor suspects that that these
students may have previous experience with pets that gives them an advantage in
the class. To test this hypothesis, the instructor gives the entire class a
questionnaire at the beginning of the course. One question determines if each
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student currently has a pet of any type at home. Based on the responses to this
question, the instructor divides the class into two groups and compares the rats’
learning scores for the two groups.
5. A scientist investigated the authenticity of extrasensory perception (ESP) by
asking subjects who claimed to have ESP to predict the symbol that would appear
on the back side of a succession of cards. Each card had a square, a circle, a star,
or a triangle. Subjects were informed of this fact and were asked to predict what
was on the back of each card as it was held up to them. Because the subjects could
not see the backs of the cards, if they had no ESP and simply guessed, they would
get an average of 0.25 answers correct (μ = 0.25). The scientist measured how
many answers the subjects got correct out of 100 cards.
6. A researcher is interested in how the values taught to students by their parents
influence their academic achievement. The parents of one group of students is
asked to follow a program in which they spend one hour per day discussing
homework assignments with their child. In the other group, parents are given no
program to follow. To control for genetic influences on academic achievement,
the subjects in the study are identical twins raised apart (i.e., by different parents).
One of the twins is randomly assigned to one group and the other twin is placed in
the other group. Academic achievement is measured by grade point average at the
end of the first year of high school.
27. Hypothesis Testing With z Tests
1. Suppose we think that listening to classical music will affect the amount of time it takes a
person to fall asleep; we conduct a study to test this idea.
a. Suppose that the average person in the population falls asleep in 15 minutes
(without listening to classical music) with σ = 6 minutes. State the null and
alternative hypotheses for this study.
b. Assume that the amount of time it takes people in the population to fall asleep is
normally distributed. In the study, we have a sample of people listen to classical
music and then we measure how long it takes them to fall asleep. Suppose the
sample of 36 people fall asleep in 12 minutes. What is the probability of obtaining
a sample mean of 12 minutes or smaller? Assuming α = 0.05, is your
calculated pvalue in the critical region? (Hint: Remember to consider two critical
regions.)
c. Using your answer above, what decision should be made about your null
hypothesis?
d. Assume now that in reality, classical music does not affect how long it takes
people to fall asleep. In this case, what kind of decision (correct, Type I error, or
Type II error) have you made in (c)?
2. A psychologist examined the effect of chronic alcohol abuse on memory. In this study, a
standardized memory test was used. Scores on this test for the general population form a
normal distribution with μ = 50 and σ = 6. A sample of n = 22 alcohol abusers had a
mean score of ¯¯¯XX¯ = 47. Is there evidence for memory impairment among alcoholics?
Use α = 0.05 for a one-tailed test. Write out each step of hypothesis testing.
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3. On a vocational interest inventory that measures interest in several categories, a very
large standardization group of adults (i.e., a population) has an average score of μ = 22
and σ = 4. Scores are normally distributed. A researcher would like to determine if
scientists differ from the general population in terms of writing interests. A random
sample of scientists is selected from the directory of a national science society. The
scientists are given the inventory, and their test scores on the literary scale are as follows:
21, 20, 23, 28, 30, 24, 23, 19. Do scientists differ from the general population in their
writing interests? Test at the 0.05 level of significance for two tails. Write out each step
of hypothesis testing.
28. Hypothesis Testing With a Single Sample
Consider the following scenarios. For each one, determine which formula (z or t) is appropriate
to use to answer the question asked. (You don’t need to do any computations.)
1. Pat, a personal trainer would like to examine the effects of humidity on exercise behavior.
It is known that the average person in the United States exercises an average of μ = 21
minutes each day. The personal trainer selects a random sample of n = 100 people and
places them in a controlled atmosphere environment where the relative humidity is
maintained at 90%. The daily amount of time spent exercising for the sample averages
18.7 minutes with s = 5.0.
2. In an attempt to regulate the profession, the U.S. Department of Fitness has developed a
fitness test for personal trainers. The test requires that the trainers must perform a series
of exercises within a certain period of time. Normative data, collected in a nationwide
test, reveal a normal distribution with an average completion time of μ = 92 minutes and
of σ = 11. Pat and four other Hollywood personal trainers (n = 5) take the test. For these
trainers, the average time to complete the task averages 115 minutes. Pat is worried that
the Hollywood personal trainers in this sample differ significantly from the norm.
3. Now let’s conduct the hypothesis tests for the examples above. Complete the hypothesis
test for the tests you choose for (1) and (2) above (z or t test), showing all the steps.
29. One-Sample t Test in SPSS
Use SPSS to complete the one-sample t test and answer the questions for each study example
below.
1. Suppose that your psychology professor, Dr. I. D. Ego, gives a 20-point true/false quiz to
nine students and wants to know if they are different from groups in the past, who have
tended to have an average of 9. Their scores from the current group are 6, 7, 7, 8, 8, 8, 9,
9, 10. Did the current group perform differently from those in the past? Assume a critical
value of α = 0.05.
2. The personnel department for a major corporation in the Northeast reported that the
average number of absences during the months of January and February last year was μ =
7.4. In an attempt to reduce absences, the company offered free flu shots to all employees
this year. For a sample of n = 10 people who took the flu shots, the number of absences
this year were 6, 8, 10, 3, 4, 6, 5, 4, 5, 6. Do these data indicate a significant reduction in
the number of absences? Use α = 0.05.
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30. One-Sample t Tests by Hand
Use a one-sample t test (calculated by hand) to answer the questions below:
1. Suppose that your psychology professor, Dr. I. D. Ego, wants to evaluate people’s driving
ability after 24 hours of sleep deprivation. She develops a test of driving skill (scores
ranging from 1 = bad driving to 10 = excellent driving) and administers it to 101 drivers
who have been paid to stay awake for 24 hrs. The scores from the group had a mean of
4.5 and a standard deviation of 1.6. Determine if the sleep-deprived group mean is
significantly different from the known population mean of 5.8 for the driving test.
Assume α = 0.05.
2. Several years ago, a school survey revealed that the average age at which students first
tried an alcoholic beverage was μ = 14 years (with a normal distribution). To determine if
anything has changed, a random sample of five students was asked questions about
alcohol use. The age at which drinking first began was reported as 11, 13, 14, 12, 10. Use
these data to determine if there has been a change in the age at which drinking began. Use
α = 0.05.
3. A random sample of n = 36 scores has ¯¯¯XX¯ = 48. Use this sample (α = 0.05) to
determine if the sample is different from the population with µ = 45 for each of the
following situations:
1. Sample SS = 60
2. Sample SS = 600
3. How does the sample variability contribute to the outcome of the test?
4. A national company is attempting to determine if they need to hire more employees. One
thing they are basing this decision on is the number of hours per week their current
employees work. They collect a sample of average hours worked per week from 30
employees to compare with the national full-time work standard of 40 hours per week.
The mean number of hours worked for their sample is 47.8 with SS = 1020. Using α =
0.05, conduct a test to determine if this company’s employees work more hours per week
than the national standard.
5. Scores on the SAT test are normally distributed with μ = 500 and σ = 100. Dr. Ed
Standards, the local district school superintendent, develops a new program that he
believes should increase SAT scores for students. He selects 25 local high school students
to participate in the program and then take the SAT test. His sample has an average SAT
score of 559. Conduct a hypothesis test to determine if this program works. Show all your
steps and state all your assumptions.
6. Suppose that the school board tells Dr. Standards that the new program is too expensive
to pilot on 25 students and asks that he reduce his sample size to 9 students. Assume the
same properties for the population of SAT scores. Suppose that his sample of 9 students
also has a mean score of 559. How does this reduction in sample size affect Dr.
Standards’s hypothesis test?
31. Related Samples t Tests
1. A major university would like to improve its tarnished image following a large oncampus scandal. Its marketing department develops a short television commercial and
tests it on a sample of n = 7 subjects. People’s attitudes about the university are measured
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with a short questionnaire both before and after viewing the commercial. The data are as
follows:
2. Person
3. X1
(Before)
4. X2
(After)
5. A
6. 15
7. 15
8. B
9. 11
10. 13
11. C
12. 10
13. 18
14. D
15. 11
16. 12
17. E
18. 14
19. 16
20. F
21. 10
22. 10
23. G
24. 11
25. 19
26. H
27. 10
28. 20
29. I
30. 12
31. 13
32. J
33. 15
34. 18
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1. Is this a within-subjects or a matched samples design? Explain your answer.
2. Conduct a hypothesis test (showing all the steps) to determine if the university
should spend money to air the commercial (i.e., did the commercial improve the
attitudes?) Assume an alpha level = 0.05.
35. For the sample difference scores below, determine if the sample differs from D = 0.
Use α = 0.01.
36. Difference scores (D): 4, 5, 4, 2, 4, 5, 3, 5, 4
37.
38. A researcher was interested in environmental effects on handedness. He measured the
handedness of twins raised apart, where a positive score indicates more right-handedness
and a negative score indicates more left-handedness (a score of zero means the subject is
ambidextrous). He used matched pairs of identical twins as subjects to rule out any
genetic contribution to handedness scores (identical twins are the same genetically). The
scores for each pair of twins are listed below. Use these data to determine if the twins
differ in handedness score (indicating that environment plays a role in handedness). Use
α = 0.05.
39.
40. Handedness Score
41. Pair
42. Twin A
43. Twin B
44. 1
45. +10
46. +11
47. 2
48. −8
49. +3
50. 3
51. −11
52. +11
53. 4
54. +15
55. +10
56. 5
57. 0
58. +8
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59. 6
60. −4
61. +7
62. Each of the following sets of sample statistics comes from a within-subjects design.
63. Set 1: n = 10, ¯¯¯DD¯ = +4.0, s = 10
64. Set 2: n = 10, ¯¯¯DD¯ = +4.0, s = 2
65.
Find t values. Without looking up the critical t, for which set is it more likely to reject the H0
indicating that the μD = 0? Why?
32. Related Samples t Test in SPSS
1. A psychology instructor teaches statistics. She wants to know if her lectures are helping
her students understand the material. She tells students to read the chapter in the textbook
before coming to class. Then, before lecturing, the professor gives her class (n = 10) a
short quiz on the material. Then she lectures on the same topic and follows her lecture
with another quiz on the same material. Is there an effect by her lecture? Assume α =
0.05. The data are as follows:
2. Person
3. X1
(Before)
4. X2
(After)
5. A
6. 85
7. 85
8. B
9. 81
10. 83
11. C
12. 70
13. 78
14. D
15. 91
16. 92
17. E
18. 84
19. 88
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20. F
21. 70
22. 70
23. G
24. 91
25. 89
26. H
27. 80
28. 90
29. I
30. 72
31. 73
32. J
33. 85
34. 88
1. Enter the data into SPSS. Test your H0 using a paired samples t test. Do you reject
the H0?
2. Use the Compute function to make a new variable that is the difference between
the after-lecture quiz and the before-lecture quiz. Now use SPSS to compute a
one-sample t test on this new difference column (use zero as your test value).
How do the results of this test compare with your earlier answer? Why do you
think this occurred?
3.
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