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

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 ${\bar{x}}_2=6.57$ 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?

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.

Perform a hypothesis test with $\alpha =0.1$ to see if there is 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 $\alpha =0.05$.

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: $n_1=25$; $x̄_1=22.4$ hours; $s_1=3.2$ hours

Company B: $n_2=16$ $x̄_2=21.1$ 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 ${\bar{x}}_2=6.57$ 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?