From the list given to you for each of the following hypothe

From the list given to you for each of the following hypothesis testing situations, indicate the test you would use and the reason (e.g. One sample test for the variance of a normal distribution)

One sample z test for the mean of a normal distribution with known variance (Test 1)

One Sample T Test for the Mean of a Normal Distribution with unknown Variance (Test 2)

The paired t-test (Test 3)

Two sample t-test for independent samples with unequal variances (Test 4)

Two sample t-test for independent samples with equal variances (Test 5)

a) Research question: Is there a difference in the students’ scores following a teaching intervention?

Ho: There is no difference in the mean pre-and-post scores

Ha: There is a difference in mean pre- and post-marks

Test?

b) A researcher wants to know if a particular sample of college students is similar to or different from college students in general. His hypothesis tests whether the average of the sample (M) suggests that the students come from a population with a known mean (m) or whether it comes from a different population.

Test?

Solution

a)

It is a TEST 3: PAIRED T TEST.

This is because we have the same students , and we are comparing pre and post scores.

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b)

It is TEST 2: One Sample T Test for the Mean of a Normal Distribution with unknown Variance.

Here, we are just testing that specific college (one sample), being compared to a population. So, we may have a limited sample size here, so we use test 2.