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Subject
Economics
School
UCI
Type
Homework
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1/8
ECON 15B
Homework
8
1. In order to compare the means of the populations, independent random samples of
400 observations are selected from each population, with the following results:
Sample 1
Sample 2
𝑥̅1 = 5,275
𝑥̅2 = 5,240
𝑠1 = 150
𝑠2 = 200
a. Use a 95% confidence interval to estimate the difference between the population means
(𝜇1 − 𝜇2). Interpret the confidence interval.
Differenc
e
n1
n2
Sample
mean
Std.
err.
L. limit
U.
limit
μ1 - μ2
400
400
35
12.5
10.5
59.5
35±10.5
We expect that 95% of the populations mean difference to be between 10.5 and 59.5.
b. Test the null hypothesis 𝐻0: (𝜇1 − 𝜇2) = 0 versus the alternative hypothesis
𝐻𝑎: (𝜇1 − 𝜇2) ≠ 0. Give the significance level of the test and interpret the result.
Two sample Z summary hypothesis test:
μ
1
: Mean of population 1 (Std. dev. = 150)
μ
2
: Mean of population 2 (Std. dev. = 200)
μ
1
- μ
2
: Difference between two means
H
0
: μ
1
- μ
2
= 0
H
A
: μ
1
- μ
2
≠ 0
Hypothesis test results:
Difference
Sample mean
Std. err.
Z-stat
P-value
μ
1
- μ
2
35
12.5
2.8
0.0051
Z=2.8,
p value=0.0052
Therefore, Reject 𝐻0
c. Suppose the test in part b was conducted with the alternative hypothesis 𝐻𝑎: (𝜇1 − 𝜇2)
> 0. How would your answer to part b change?
Differenc
e
n<sub>1</sub
>
n<sub>2</sub
>
Sample
mean
Std.
err.
Z-stat
P-value
μ1 - μ2
400
400
35
12.5
2.8
0.00255
5
P value =0.0026

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ECON 15B
d. Test the null hypothesis 𝐻0: (𝜇1 − 𝜇2) = 25 vs 𝐻𝑎: (𝜇1 − 𝜇2) ≠ 25. Give the
significance level and interpret the result. Compare your answer to the test
conducted in part b.
424.0212.02
8.0
35
200
86
150
25-35
n
s
n
s
)()x-x(
22
2
2
2
1
2
1
2121
==
=
+
=
+
−−
=
p
z
z
Z=0.8
P value=0.424 Therefore, do not reject 𝐻0
e. What assumptions are necessary to ensure the validity of the inferential procedures
applied in parts a-d?
It must be an independent random sample
2. Some college professors make bound lecture notes available to their classes in an effort
to improve teaching effectiveness. In a study, two groups of students were surveyed – 86
students enrolled in a promotional strategy class that required the purchase of lecture
notes and 35 students enrolled in a sales/retailing elective that did not offer lecture notes.
At the end of the semester, students were asked to respond to the statement, “Having a
copy of the lectrure notes was (would be) helpful in understanding the material.”
Responses were measured on a 9- point semantic difference scale, where 1=strongly
disagree and 9=strongly agree.
Purchased Lecture Notes
Did Not Purchase Lecture Notes
𝑛1=86
𝑛2=35
𝑥̅1 = 8.48
𝑥̅2 = 7.80
𝑠
2
= 0.94
1
𝑠
2
= 2.99
2
a. Describe the two populations involved in the comparison.
The population included two groups of students. Group 1 comprised of 86 students enrolled in a
promotional strategy class that required the purchase of lecture notes. Group 2 comprised of 35
students enrolled in a sales/retailing elective that did not offer lecture notes.

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ECON 15B Homework 8 1. In order to compare the means of the populations, independent random samples of 400 observations are selected from each population, with the following results: Sample 1 Sample 2 𝑥̅1 = 5,275 𝑥̅2 = 5,240 𝑠1 = 150 𝑠2 = 200 a. Use a 95% confidence interval to estimate the difference between the population means (𝜇1 − 𝜇2). Interpret the confidence interval. Differenc Sample Std. U. e n1 n2 mean err. L. limit limit μ1 - μ2 400 400 35 12.5 10.5 59.5 35±10.5 We expect that 95% of the populations mean difference to be between 10.5 and 59.5. b. Test the null hypothesis 𝐻0: (𝜇1 − 𝜇2) = 0 versus the alternative hypothesis 𝐻𝑎: (𝜇1 − 𝜇2) ≠ 0. Give the significance level of the test and interpret the result. Two sample Z summary hypothesis test: μ1 : Mean of population 1 (Std. dev. = 150) μ2 : Mean of population 2 (Std. dev. = 200) μ1 - μ2 : Difference between two means H0 : μ1 - μ2 = 0 HA : μ1 - μ2 ≠ 0 Hypothesis test results: Difference n1 n2 Sample mean Std. err. Z-stat P-value μ1 - μ2 400 400 35 12.5 2.8 0.0051 Z=2.8, p value=0.0052 Therefore, Reject 𝐻0 c. Suppose the test in part b was conducted with the alternative hypothesis 𝐻𝑎: (𝜇1 − 𝜇2) > 0. How would your answer to part b change? Differenc n1 mean err. μ1 - μ2 P value =0.0026 400 400 35 12.5 Z-stat P-value 0.00255 2.8 5 ECON 15B d. Test the null hypothesis 𝐻0: (𝜇1 − ? ...
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