STATISTICS
Name: Benedict V. Cruz
Date: December 18, 2021
Final Exam
1. With the growth of internet service providers, a researcher decides to examine whether there is a
correlation between cost of internet service per month (rounded-off values) and degree of customer
satisfaction (on a scale of 1 - 10 with a 1 being not at all satisfied and a 10 being extremely satisfied).
The researcher only includes programs with comparable types of services. A sample of the data is
provided below.
Cost
11
Satisfaction 6
18
8
17
10
15
4
9
9
5
6
12
3
9
5
22
2
25
10
a) What is the coefficient of correlation? 0.0 < 𝟎. 𝟏𝟓 < 0.2 very weak correlation
b) What does this statistic mean concerning the relationship between amount of money spent per
month on internet provider service and level of customer satisfaction? The amount of money
spent per month on internet service provider service has a very weak correlation to
the level of customer satisfaction.
c) What percent of the variability is accounted for by the relation of these two variables? 2.4%
2. The following table shows 10 weeks of sales of two competing brands of athletic shoes (in pairs) at
a sporting goods store:
Brand A
Brand B
76
172
58
134
63
140
71
159
66
145
55
126
60
132
64
141
69
150
80
178
Predict the sales of Brand B shoes for a week in which the sales of Brand A shoes are 65 pairs.
𝟏𝟒𝟓. 𝟏𝟐 𝐩𝐚𝐢𝐫𝐬 ≈ 𝟏𝟒𝟔 𝒑𝒂𝒊𝒓𝒔
3. A farmer thinks that a new type of organic feed may lead to plumper chickens. As every farmer
knows, a fat chicken sells for more than a thin chicken. A chicken on standard feed weighs an average
of 3 pounds. The farmer feed a sample of 25 chickens the organic feed for several weeks. The average
weight of a chicken on the new organic feed is 3.49 pounds with a standard deviation of 0.90 pounds.
Should the farmer switch to the organic feed? Justify you answer.
4. Eight individuals indicated their attitudes toward socialized medicine before and after listening to a
pro-socialized medicine lecture. Attitudes were assessed on a scale from 1 to 7, with higher scores
indicating more positive attitudes. The attitudes before and after listening to the lecture were as
indicated in the second and third columns of the table. Test for a relationship between the time of
assessment and attitudes toward socialized medicine.
Individual
1
2
3
4
5
6
7
8
Before
Lecture
3
4
3
5
2
5
3
4
After
Lecture
6
6
3
7
4
6
7
6
a) What is the computed t? Critical t-value?
b) What would be the null hypothesis in this
study?
c) What would be the alternative hypothesis?
d) Interpret the results.
5. Researches compared two weight loss supplements. Two independent groups of 15 randomly
selected participants took each supplement, and researches recorded the amount of weight lost in a
month. Conduct a test to determine if the two brands are equal. Use an alpha level of .05.
Brand A
6.8
13.2
8.8
7.2
10.5
2.1
7.4
13.6
7.3
9.8
6.6
7.1
13.7
14.2
6.8
Brand B
4.7
11.4
6.7
5
8.6
2
1.5
11.8
5.1
7.8
4.4
4.9
11.9
12.4
4.8
a) What is the computed t? Critical t-value?
b) What would be the null hypothesis in this
study?
c) What would be the alternative hypothesis?
d) Interpret the results.
6. In a test of the ability of a certain polymer to remove toxic wastes from water, experiments were
conducted at three different temperatures. The data below give the percentages of the impurities
that were removed by that polymer in different independent attempts. Test the hypothesis that the
polymer performs equally well at three temperatures. Use an alpha level of .05.
Low Temperature
42
41
37
29
35
40
32
a)
b)
c)
d)
Medium Temperature
36
35
32
38
39
42
34
What is the computed F? Critical F-value?
What would be the null hypothesis in this study?
What would be the alternative hypothesis?
Interpret the results.
High Temperature
33
44
40
36
44
37
45