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 $\alpha =0.01$.

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

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=0.05 , n1=7 , n2=11

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=0.01 , n1=19 , n2=22

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=30 , n2=32