10. Hypothesis Testing for Two Samples

When comparing two independent samples with unknown and unequal variances, which of the following statements is NOT true?

Suppose two independent random samples are taken from two normal populations with unknown and unequal variances. Which statistical test is most appropriate for testing whether the population means are equal?

When dealing with two independent means where the population variances are unknown and assumed to be unequal, which statistical test is most appropriate to compare the means?

Perform a hypothesis test with $\alpha =0.1$ to see if there's evidence that ${\mu }_1\ne {\mu }_2$.

Researchers are comparing the average number of hours worked per week by employees at two different companies. Below are the results from two independent random samples. Assuming population standard deviations are unknown and unequal, calculate the $t$-score for the difference in means, but do not find a $P$-value or state a conclusion.

Company A: $n_1=25$; ${\bar{x}}_1=22.4$ hours; $s_1=3.2$ hours

Company B: $n_2=16$ ${\bar{x}}_2=21.1$ hours; $s_1=2.9$ hours

A researcher is comparing average number of hours spelt per night by college students who work part-time versus those who don't. From survey data, they calculate ${\bar{x}}_1=6.82$ hours and $x_{\bar{2}}=6.57$ hours with a margin of error of 0.41. Should they reject or fail to reject the claim that there is no difference in hours slept between the two groups?

Create a confidence interval with $\alpha =0.1$ for the difference between the 2 population means to see if there's evidence that ${\mu }_1\ne {\mu }_2$.

For ${\bar{x}}_1=29,S_{x1}=3.3,n_1=40,{\bar{x}}_2=26,S_{x2}=3.8$, & $n_2=75$, create a confidence interval for the difference of the two means to test if there's evidence that ${\mu }_1>{\mu }_2$ for $\alpha =0.05$.

For ${\bar{x}}_1=44,S_{x1}=2.3,n_1=50,{\bar{x}}_2=40,S_{x2}=3.1$, & $n_2=75$, test if there is evidence that ${\mu }_1>{\mu }_2$ for $\alpha =0.01$ using a hypothesis test.