10. Hypothesis Testing for Two Samples

For ${\bar{x}}_1=41,S_{x1}=8.3,n_1=40,{\bar{x}}_2=39,S_{x2}=5.8$, & $n_2=50$, perform a hypothesis test to test the claim that ${\mu }_1>{\mu }_2$, assuming ${\sigma }_1={\sigma }_2$ for $\alpha =0.01$.

In Exercises 11–16, test the claim about the difference between two population means μ1 and μ2 at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed.

Claim: μ1>= μ2; α=0.01. Assume (σ1)^2 = (σ2)^2

Sample statistics: x̅1= 44.5, s1= 5.85, n1= 17 and x̅2= 49.1, s2= 5.25, n2= 18

Find the critical value(s) for the alternative hypothesis, level of significance , and sample sizes and . Assume that the samples are random and independent, the populations are normally distributed, and the population variances are (a) equal

Ha:μ1≠μ2 , α=0.10 , n1=11 , n2=14