Independent random samples of 36 and 41 observations are drawn from two quantita
ID: 3314192 • Letter: I
Question
Independent random samples of 36 and 41 observations are drawn from two quantitative populations, 1 and 2, respectively. The sample data summary is shown here.
Do the data present sufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2? Use one of the two methods of testing presented in this section. (Round your answer to two decimal places.)
z =
Explain your conclusions.
H0 is rejected. There is sufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2.H0 is not rejected. There is sufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2. H0 is rejected. There is insufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2.H0 is not rejected. There is insufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2.
Sample 1 Sample 2 Sample Size 36 41 Sample Mean 1.29 1.31 Sample Variance 0.0550 0.0510Explanation / Answer
The statistical software output for this problem is:
Two sample T summary hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 < 0
(without pooled variances)
Hypothesis test results:
Hence,
z = -0.38
H0 is not rejected. There is insufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2.
Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 -0.02 0.052646749 72.906283 -0.3798905 0.3526