Question

A teacher wants to test whether his students will perform better on their exam if the room where they take the exam is cooled to a freezing temperature. On the day of an exam, he randomly assigned his class into two groups. One group took the exam under regular conditions and one group took the exam in a freezing cold room. After the exam, the teacher calculated the average score in each group. Assume that all conditions for inference have been met. Which of these is the most appropriate test and alternative hypothesis?.

Answer 1

Considering the situation described in the text, we have that:

• A two-sample t-test is used.

• The null hypothesis is $H_0: \mu_F - \mu_R = 0$.

• The alternative hypothesis is $H_1: \mu_F - \mu_R > 0$.

In this problem, we consider that:

• $\mu_R$ is the mean score of students who took the exam in regular conditions.

• $\mu_F$ is the mean score of students who took the exam in freezing cold conditions.

What are the hypothesis tested?

At the null hypothesis, we test if both groups have the same mean score, that is, the subtraction of the means is of 0, hence:

$H_0: \mu_F - \mu_R = 0$

At the alternative hypothesis, we test if students that did the test in freezing cold conditions performed better, that is, the subtraction is positive, hence:

$H_1: \mu_F - \mu_R > 0$.

We have the comparison(subtraction) of two samples, and we have the standard deviation for each sample, not for the population, hence a two-sample t-test is used.

More can be learned about an hypothesis test at https://brainly.com/question/26454209