Description
Econ 15B question. Most of them are computational problems. Econ major chooses me.
Explanation & Answer
Here you go
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
π 1 = 150
π 2 = 200
a. Use a 95% confidence interval to estimate the difference between the population means
(π1 β π2). Interpret the confidence interval.
n 1 = 400
x 1 = 5275 s1 = 150
n 2 = 400
x 2 = 5240
s 2 = 20
ο‘ = 0.05
z = 1.96
CI = ( x 1 - x 2 ) ο± Z ο‘ ο΄ (
2
s12 s 22
+ )
n1 n2
150 2 200 2
= (5275 β 5240) ο± 1.96 ο΄ (
+
)
400
400
= 35 ο± 24.5
Lower bound = 10.5
Upper Bound = 59.5
b. Test the null hypothesis π»0: (π1 β π2) = 0 versus the alternative hypothesis
π»π: (π1 β π2) β 0. Give the significance level of the test and interpret the result.
H ο‘ : ο1 β ο 2 οΉ 0
Two tailed test
x1 - x 2
Z=
s12 s 22
+
n1 n 2
=
5275 β 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: (π1 β π2) > 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 β 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 populationβs mean.
2
d. Test the null hypothesis π»0: (π1 β π2) = 25 vs π»π: (π1 β π2) 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 ) β ( ο1 β ο 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...