For each of the following scenarios, select ALL of the statistical tests that would be appropriate to answer the question of interest.

$($a$)$ Researchers would like to compare the effectiveness of two sleep aid drugs. They had $20$ people who take drug A and $20$ people who take drug B report the number of hours of sleep they get each night. Both sets of data are approximately normal and have similar variances.

Welch t$-$test

Paired t$-$test

Equal variance two$-$sample t$-$test

Sign test

Points possible: $2$

$($b$)$ A teacher wants to know how many books her students read each month, on average. She chooses $10$ students at random and asks each one how many books they read each month. The data is very right$-$skewed.

One$-$sample t$-$test

One$-$sample z$-$test

One$-$sample bootstrap test

Sign test

Points possible: $2$

$($c$)$ A city official is interested in evaluating the quality of internet service in her city. She takes a random sample of $150$ households, and asks each one to describe their internet speed as either "Slow", "Acceptable", or "Fast".

Chi$-$squared goodness$-$of$-$fit test

Chi$-$squared test for independence

Analysis of variance

Linear regression

Points possible: $2$

$($d$)$ A store manager would like to know whether his customers spend more on raw ingredients or pre$-$made meals. He takes a random sample of $100$ customers and records how much they spent on raw ingredients and how much they spent on pre$-$made meals.

Analysis of variance

Wilcoxon signed$-$rank test

Paired t$-$test

Welch t$-$test

Points possible: $2$