Homework SourseA sample of 38 observations is selected from one population
A sample of 38 observations is selected from one population with a population standard deviation of 4.9. The sample mean is 102.0. A sample of 49 observations is selected from a second population with a population standard deviation of 4.8. The sample mean is 100.4. Conduct the following test of hypothesis using the 0.04 significance level.
State the decision rule. (Negative values should be indicated by a minus sign. Round your answer to 2 decimal places.)
| A sample of 38 observations is selected from one population with a population standard deviation of 4.9. The sample mean is 102.0. A sample of 49 observations is selected from a second population with a population standard deviation of 4.8. The sample mean is 100.4. Conduct the following test of hypothesis using the 0.04 significance level. |
| H0 : 1 = 2 |
| H1 : 1 2 |
Solution
a) Two tailed test
b) IF p <0.04 reject null hypothesis
Or reject H0 if |Z|>2.06
c)
z for 96% CI= 2.05
declare p larger than alpha=0.04 not significant.
mean1 eq: 102 (variance= 24.01) (se= 0.079)
mean2 eq: 100.4 (variance= 23.04) (se= 0.6857)
Difference between means:
M1-M2=102-100.4=1.6
sd=4.8456; se=0.6902
96% CI of difference:
0.1824 <1.6< 3.0176
z-difference: 2.318
As z>2.06 reject null hypothesis.
