Statistics Problems
Last name:
First name:
For each of the following problems, use the information provided and/or the normal curve below to find a solution. You do not
need to show HOW you found a mean (x) or sample standard deviation (s), since those are done using calculator functions, but all
other calculations should have work shown.
1.
Professor Halen has 184 students in his college mathematics lecture class. The scores on the midterm exam are normally
distributed with a mean of 72.3 and a standard deviation of 8.9. How many students in the class can be expected to receive
a score between 82 and 90? Express answer to the nearest student.
2.
Residents of upstate New York are accustomed to large amounts of snow with snowfalls often exceeding 6 inches in one
day. In one city, such snowfalls were recorded for two seasons and are as follows (in inches):
8.6
11.5
9.0
7.7
8.5
8.0
9.5
7.0
6.7
6.8
14.4
9.2
14.1
8.4
21.5
6.1
6.1
7.1
What are the mean and the population standard deviation for this data, to the nearest hundredth?
3.
Neesha's scores in Chemistry this semester were rather inconsistent: 100, 85, 55, 95, 75, 100. For this population, how
many scores are within one standard deviation of the mean?
4.
From 1984 to 1995, the winning scores for a golf tournament were 276, 279, 279, 277, 278, 278, 280, 282, 285, 272, 279,
and 278. Using the standard deviation for this sample, find the percent of these winning scores that fall within one
standard deviation of the mean.
A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. A pilot
study was conducted to examine this hypothesis. Ten older adults (over the age of 70) and ten younger adults (between 20 and 30)
were give a life satisfaction test (known to have high reliability and validity). Scores on the measure range from 0 to 60 with high
scores indicative of high life satisfaction; low scores indicative of low life satisfaction. The data are presented below. Compute the
appropriate t-test.
Perceived life satisfaction
Mean
Std. Dev.
Older adults
45
38
52
48
25
39
51
46
55
46
44.5
8.68267752
Younger adults
34
22
15
27
37
41
24
19
26
36
28.1
8.54335349
1. What would be the null hypothesis in this study?
There will be no difference between older and younger adults on perceived life satisfaction.
2. Fill in the information below:
a. p: 0.000473911
b. Circle one: p < 0.05 p > 0.05
3. Is there a significant difference between the two groups? Yes
4. What conclusion can you draw? Support with the reason you made the decision!
We reject the null hypothesis and conclude that there IS a significant difference between younger and older adults in
perceived life satisfaction because p was less than 0.05 on the t-test.
5. In the space below, graph the means and draw error bars to show standard deviation. Label your axes!
Perceived life
satisfaction scores
60
50
40
30
20
10
0
Older adults
Younger adults
A researcher hypothesizes that electrical stimulation of the lateral habenula will result in a decrease in food intake (in this case,
chocolate chips) in rats. Rats undergo stereotaxic surgery and an electrode is implanted in the right lateral habenula. Following a
ten day recovery period, rats (kept at 80 percent body weight) are tested for the number of chocolate chips consumed during a 10
minute period of time both with and without electrical stimulation. Compute the appropriate t-test for the data provided below.
Number of chocolate
chips consumed (per 10
mins)
Number of chocolate chips consumed per 10 minutes
Mean
Std. Dev.
Stimulation
12
7
3
11
8
5
14
7
9
10
8.6
3.30655914
No Stimulation
8
7
4
14
6
7
12
5
5
8
7.6
3.16929715
1. What would be the null hypothesis in this study?
There will be no difference between the amount of chocolate chips eaten based on whether or not the stimulus happens.
2. Fill in the information below:
a. p: 0.49874576
b. Circle one: p < 0.05 p > 0.05
3. Is there a significant difference between the two groups? No
4. What conclusion can you draw? Support with the reason you made the decision!
Because p>0.05, we accept the null hypothesis that there is no significant difference between the two groups.
5. In the space below, graph the means and draw error bars to show standard deviation. Label your axes!
14
12
10
8
6
4
2
0
Stimulation No Stimulation
Twelve cars were equipped with radial tires and driven over a test course. Then the same 12 cars (with the same drivers) were
equipped with regular belted tires and driven over the same course. After each run, the cars’ gas economy (in km/l) was measured.
Is there evidence that radial tires produce better fuel economy?
Gas Economy (km/L)
Car
Mean
Std. Dev.
Radial Tires
4.2 4.7
6.6
7.0
6.7
4.5
5.7
6.0
7.4
4.9
6.1
5.2
5.75
1.05270215
Belted tires
4.1 4.9
6.2
6.9
6.8
4.4
5.7
5.8
6.9
4.7
6.0
4.9 5.608333 0.99403524
1. What would be the null hypothesis in this study?
There will be no significant difference between the gas economy of cars with radial or belted tires.
2. Fill in the information below:
a. p: 0.737873447
b. Circle one: p < 0.05 p > 0.05
3. Is there a significant difference between the two groups? NO
4. What conclusion can you draw? Support with the reason you made the decision!
We accept the null hypothesis because p>0.05, there is no significant difference between gas economy for cars with radial or
belted tires.
5. In the space below, graph the means and draw error bars to show standard deviation. Label your axes!
8
6
4
2
0
Radial Tires
Belted tires
Sam Sleepresearcher hypothesizes that people who are allowed to sleep for only four hours will score significantly lower than
people who are allowed to sleep for eight hours on a cognitive skills test. He brings sixteen participants into his sleep lab and
randomly assigns them to one of two groups. In one group he has participants sleep for eight hours and in the other group he has
them sleep for four. The next morning he administers the SCAT (Sam's Cognitive Ability Test) to all participants. (Scores on the SCAT
range from 1-9 with high scores representing better performance).
SCAT score
Mean
Std. dev.
8 hrs. sleep
5
7
5
3
5
3
3
9
5
2.138089935
4 hrs. sleep
8
1
4
6
6
4
1
2
4
2.563479778
1. What would be the null hypothesis in this study?
There is no significant different between the 8 and 4 hours of sleep with scores on a cognitive skill test.
2. Fill in the information below:
a. p: 0.4115204
b. Circle one: p < 0.05 p > 0.05
3. Is there a significant difference between the two groups? NO
4. What conclusion can you draw? Support with the reason you made the decision!
We accept the null hypothesis because p>0.05, there is no significant difference in the test scores of people who get 8
hours or 4 hours of sleep.
5. In the space below, graph the means and draw error bars to show standard deviation. Label your axes!
Cognitive Skills Test
Scores
8
6
4
2
0
8 hrs. sleep
4 hrs. sleep
A laboratory study was conducted to investigate whether wind speed affects the diameter of the web that orb spiders produce.
Therefore, the scientists exposed 20 spiders to low wind speeds (5 km/hr) and another 20 spiders to high wind speeds (15 km/hr) in
individual containers. Several days later, the scientists determined the diameter (in mm) of the webs spun by each spider; one spider
did not spin a web. Is there a significant difference in the mean diameter of webs spun at high versus low wind speeds?
Diameter of webs spun by spiders (mm)
Low
wind
High
wind
68
98
99
88
78
91
69
91
83
83
74
57
91
91
97
87
80
84
73
80
60
80
58
49
52
47
92
76
79
88
89
51
72
95
62
75
63
59
53
Mean
Std. Dev.
81.75
12.88767261
69.84211
15.40657564
Spider web diameter
(mm)
1. What would be the null hypothesis in this study?
There will be no relationship between the diameter of webs spun by spiders in high or low wind.
2. Fill in the information below:
a. p: 0.013177698
b. Circle one: p < 0.05 p > 0.05
3. Is there a significant difference between the two groups? YES
4. What conclusion can you draw? Support with the reason you made the decision!
We reject the null hypothesis because p < 0.05, there IS a significant difference in the diameter of spider webs in different
winds.
5. In the space below, graph the means and draw error bars to show standard deviation. Label your axes!
100
80
60
40
20
0
Low wind
High wind
An experiment was conducted to determine if growth of a reef-dwelling sponge differed significantly between sponges growing on
the top versus the side of the reef. Two tissue samples of equal volume (each 30 cm3) were removed from each of 17 randomly
chosen sponges. One tissue sample from each individual sponge was fixed to the top of 17 reefs and the second sample from the
same individual sponge was fixed to the side of another 17 reefs (34 reef sites in all). After three months, the volume of each sponge
tissue was re-measured and those data are given below. Does orientation on the reef (top vs. side) significantly affect the growth of
sponges?
Volume of
sponges (cm3)
Volume of sponge (cm3)
Mean Std. Dev.
Top of reef
41 33 43 42 57 45 43 48 37 44 47 32 65 61 55 44 44
Side of reef
41 40 43 44 42 47 48 42 40 41 39 41 37 47 45 46 38
1. What would be the null hypothesis in this study?
There will be no relationship between the orientation of sponges on the reef and the volume of the sponges.
2. Fill in the information below:
a. p: 0.146424321
b. Circle one: p < 0.05 p > 0.05
3. Is there a significant difference between the two groups? NO
4. What conclusion can you draw? Support with the reason you made the decision!
Because p>0.05, we accept the null hypothesis that there is no difference in the volume of sponges based on which side of
the reef they are on.
5. In the space below, graph the means and draw error bars to show standard deviation. Label your axes!
60
40
20
0
Top of reef
Side of reef
A research study was conducted to examine the clinical efficacy of a new antidepressant. Depressed patients were randomly
assigned to one of three groups: a placebo group, a group that received a low dose of the drug, and a group that received a
moderate dose of the drug. After four weeks of treatment, the patients completed the Beck Depression Inventory. The higher the
score, the more depressed the patient.
2.
3.
4.
5.
6.
50
Back Depression Inventory Scores
1.
Beck Depression inventory scores
Mean
Std. dev.
Placebo
38
47
39
25
42
38.2
8.1670068
Low dose
22
19
8
23
31
20.6
8.32466216
Moderate dose
14
26
11
18
5
14.8
7.85493475
What would be the null hypothesis in this study? There is no significant difference between the different drugs and the
back depression inventory score.
What would be the alternate hypothesis?
Fill in the information below:
a. p: 0.001760645
b. Circle one: p < 0.05 p > 0.05
Is there a significant difference between the groups? YES
If there is a significant difference, where specifically are the differences? This is not necessary, but you would conduct a ttest between each combination of pairs to see where it is.
What conclusion can you draw? Support with the reason you made the decision!
Because p<0.05 we reject the null hypothesis that there is no significant difference between two of the groups in the study.
Placebo/low-dose: p = 0.009723635
Placebo/moderate-dose: p = 0.001722353
Low-dose/moderate-dose: p = 0.290083283
Because p<0.05 between the placebo and either dose, but is >0.05 between the doses, we can conclude that any medicine
is better than the placebo, but there is not a significant difference between low- and moderate- doses.
45
40
35
30
25
20
15
10
5
0
Placebo
Low dose
Moderate dose
A researcher is concerned about the level of knowledge possessed by university students regarding United States history. Students
completed a high school senior level standardized U.S. history exam. Major for students was also recorded. Data in terms of percent
correct is recorded below for 32 students.
1.
2.
3.
4.
5.
6.
US History Exam score
Mean Std. dev.
Education
62
81
75
58
67
48
26
36
Business/Management
72
49
63
68
39
79
40
15
Behaviorhal/Social science
42
52
31
8
22
71
68
76
Fine Arts
80
57
87
64
28
29
62
45
What would be the null hypothesis in this study?
What would be the alternate hypothesis?
Fill in the information below:
a. p:
b. Circle one: p < 0.05 p > 0.0
Is there a significant difference between the groups?
If there is a significant difference, where specifically are the differences? This is not necessary, but you would conduct a ttest between each combination of pairs to see where it is.
What conclusion can you draw? Support with the reason you made the decision!
Neuroscience researchers examined the impact of environment on rat development. Rats were randomly assigned to be raised in
one of the four following test conditions: Impoverished (wire mesh cage - housed alone), standard (cage with other rats), enriched
(cage with other rats and toys), super enriched (cage with rats and toys changes on a periodic basis). After two months, the rats
were tested on a variety of learning measures (including the number of trials to learn a maze to a three perfect trial criteria), and
several neurological measure (overall cortical weight, degree of dendritic branching, etc.).
1.
2.
3.
4.
5.
6.
Beck Depression inventory scores
Mean
Std. dev.
Impoverished
22
19
15
24
18
Standard
17
21
15
12
19
Enriched
12
14
11
9
15
Super-enriched
8
7
10
9
12
What would be the null hypothesis in this study?
What would be the alternate hypothesis?
Fill in the information below:
a. p:
b. Circle one: p < 0.05 p > 0.0
Is there a significant difference between the groups?
If there is a significant difference, where specifically are the differences? This is not necessary, but you would conduct a ttest between each combination of pairs to see where it is.
What conclusion can you draw? Support with the reason you made the decision!