Quantitative Analysis � International and Public Affairs
This document covers quantitative analysis methods applied to international and public affairs.
Elijah Nelson
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Quantitative Analysis – International and Public Affairs
U6500 Sections 1, 2, 3, 4/Fall 2015
Professor Yang
Homework #8: Inference for one mean, Difference in two means, one proportion,
and Difference in two proportions
Due in Mailbox 49 6th Floor IAB:
Wednesday November 11 4:00 p.m. (Sections 3 & 4)/
Thursday November 17 4:00 p.m. (Sections 1 & 2)
52 points total
1. (8 points total) Bags of a certain brand of tortilla chips claim to have a net weight of 14
oz. Net weights actually vary slightly from bag to bag. Assume net weights are Normally
distributed. A representative of a consumer advocate group wishes to see if there is any
evidence that the mean net weight is less than advertised and so intends to test the
hypotheses H0:
= 14 versus Ha:
< 14. To do this, he selects 16 bags of tortilla chips
of this brand at random and determines the net weight of each. He finds a sample mean
of 13.88 oz. with a sample standard deviation of 0.24 oz.
a. What is the value of the test statistic?
13.88 14
Test statistic, 2
0.24 16
x
t s n
b. What is the critical value at the .05 significance level for this test? Infer the p-
value from the table.
The critical value at the .05 significance level for this test is –1.753.
The p-value is in between 0.025 and 0.05.
c. What is your conclusion (again, assume significance level of .05)? Briefly
explain your conclusion (citing your observed test statistic and p-value and what
you are comparing these against).
Since the observed test statistic, t = –2 < –1.753, reject the null hypothesis at
.05 level.
The reported results provide enough evidence to conclude that the mean net
weight is less than advertised, t (15) = –2.00, p = .032 < .05.
2. (8 points total) A researcher wished to compare the average amount of time spent in
extracurricular activities by high school students in a suburban school district with that in
a school district of a large city. The researcher obtained a simple random sample of 60
high school students in a large suburban school district and found the mean time spent in
Quantitative Analysis – International and Public Affairs
U6500 Sections 1, 2, 3, 4/Fall 2015
Professor Yang
Homework #8: Inference for one mean, Difference in two means, one proportion,
and Difference in two proportions
Due in Mailbox 49 6th Floor IAB:
Wednesday November 11 4:00 p.m. (Sections 3 & 4)/
Thursday November 17 4:00 p.m. (Sections 1 & 2)
52 points total
1. (8 points total) Bags of a certain brand of tortilla chips claim to have a net weight of 14
oz. Net weights actually vary slightly from bag to bag. Assume net weights are Normally
distributed. A representative of a consumer advocate group wishes to see if there is any
evidence that the mean net weight is less than advertised and so intends to test the
hypotheses H0:
= 14 versus Ha:
< 14. To do this, he selects 16 bags of tortilla chips
of this brand at random and determines the net weight of each. He finds a sample mean
of 13.88 oz. with a sample standard deviation of 0.24 oz.
a. What is the value of the test statistic?
13.88 14
Test statistic, 2
0.24 16
x
t s n
b. What is the critical value at the .05 significance level for this test? Infer the p-
value from the table.
The critical value at the .05 significance level for this test is –1.753.
The p-value is in between 0.025 and 0.05.
c. What is your conclusion (again, assume significance level of .05)? Briefly
explain your conclusion (citing your observed test statistic and p-value and what
you are comparing these against).
Since the observed test statistic, t = –2 < –1.753, reject the null hypothesis at
.05 level.
The reported results provide enough evidence to conclude that the mean net
weight is less than advertised, t (15) = –2.00, p = .032 < .05.
2. (8 points total) A researcher wished to compare the average amount of time spent in
extracurricular activities by high school students in a suburban school district with that in
a school district of a large city. The researcher obtained a simple random sample of 60
high school students in a large suburban school district and found the mean time spent in
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Subject
Economics