ECON15B UCI Means of The Populations, Independent Random Samples Questions

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Economics

econ15b

University of California Irvine

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Econ 15B question. Most of them are computational problems. Econ major chooses me.

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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
π‘₯Μ…1 = 5,275
π‘₯Μ…2 = 5,240
𝑠1 = 150
𝑠2 = 200
a. Use a 95% confidence interval to estimate the difference between the population means
(πœ‡1 βˆ’ πœ‡2). Interpret the confidence interval.

n 1 = 400

x 1 = 5275 s1 = 150

n 2 = 400

x 2 = 5240

s 2 = 20

 = 0.05
z = 1.96
CI = ( x 1 - x 2 ) ο‚± Z  ο‚΄ (
2

s12 s 22
+ )
n1 n2

150 2 200 2
= (5275 βˆ’ 5240) ο‚± 1.96 ο‚΄ (
+
)
400
400
= 35 ο‚± 24.5
Lower bound = 10.5
Upper Bound = 59.5
b. Test the null hypothesis 𝐻0: (πœ‡1 βˆ’ πœ‡2) = 0 versus the alternative hypothesis
π»π‘Ž: (πœ‡1 βˆ’ πœ‡2) β‰  0. Give the significance level of the test and interpret the result.

H  : 1 βˆ’  2 ο‚Ή 0
Two tailed test
x1 - x 2
Z=
s12 s 22
+
n1 n 2
=

5275 βˆ’ 5240
2

2

=

35
= 2.8
12.5

150
200
+
400
400
P value = 2 ο‚΄ 0.0026 = 0.0052
Since P is less than or equal to the level of significan ce, reject the null hypotheses
1

c. Suppose the test in part b was conducted with the alternative hypothesis π»π‘Ž: (πœ‡1 βˆ’ πœ‡2) > 0.
How would your answer to part b change?

z=

=

x1 - x 2
s12 s 22
+
n1 n 2
5275 - 5240

= 2.8
150 2 200 2
+
86
35
p = 1 βˆ’ 0.9975 = 0.0025
The value of p is less than the level of significance, therefore we reject the null hypothesis.

We can infer that the mean of population is greater than the second population’s mean.

2

d. Test the null hypothesis 𝐻0: (πœ‡1 βˆ’ πœ‡2) = 25 vs π»π‘Ž: (πœ‡1 βˆ’ πœ‡2) β‰  25. Give the significance
level and interpret the result. Compare your answer to the test conducted in part b.

z=

z=

(x 1 - x 2 ) βˆ’ ( 1 βˆ’  2 )
s12 s 22
+
n1 n 2
35 - 25

= 0 .8
150 2 200 2
+
86
35
p = 2 ο‚΄ 0.212 = 0.424

p-value is greater than level of significance, therefore we fail to reject null hypothesis. This means that
there is no significant difference between the two means.

e. What assum...


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