Question

Consider the following summary statistics, calculated from two independent random samples taken from normally distributed populations. Sample 1 F1 = 22.49 11 = 2.54 P1 = 15 Sample 2 F2 = 27.31 3 = 3.08 P2 = 18 Test the null hypothesis HO : H1 = 2 against the alternative hypothesis HA: MI <H2 a) To save you on calculations, I will tell you that the standard error of the difference in sample means (SE(X_1 bar - X_2 bar)) is 0.58876. Calculate the statistic for the pooled-variance t procedure. Round your response to at least 3 decimal places. -8.187 b) Determine the range in which the p-value falls: o p-value > 0.10 0.05 <p-value <0.10 0.025 <p-value < 0.05 0.01 <p-value <0.025 o p-value <0.01 c) What is the most appropriate conclusion that can be made? There is sufficient evidence to reject the null hypothesis at the 5% level of significance, but not at the 1% level of significance. There is insufficient evidence to reject the null hypothesis at both the 5% and 1% level of significance. There is sufficient evidence to reject the null hypothesis at both the 5% and 1% level of significance. There is sufficient evidence to reject the null hypothesis at the 1% level of significance, but not at the 5% level of significance.

Answer 1

The statistic software output for this problem is:

Two sample T summary hypothesis test: Hi : Mean of Population 1 U2 : Mean of Population 2 H1 - H2 : Difference between two means Ho: V1 - H2 = 0 HA: 41 - H2 <0 (with pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. DF T-Stat P-value H1 - 2 -4.82 0.58875971 31 -8.1867015 <0.0001

(a) t = -8.187

(b) The range of p-value is :

P-value < 0.01

The conclusion is :

There is sufficient evidence to reject the null hypothesis at both the 5% and 1% level of significance.