Question

What is the single best type of statistical analysis to use to answer?

1. Are depression scores lower after therapy than before therapy?
2. Do people own more pairs of workout shoes than dress shoes?
3. Is gender related to college major selection?

Answer 1

What is the single best type of statistical analysis to use to answer?

a. Are depression scores lower after therapy than before therapy?

Answer: Paired t-test

Explanation:

For the given samples, there is a one-to-one relationship exists between the observations of the both samples. It is observed that both samples are dependent samples. Given data is a paired data. There is a before after type relationship exists between the data. The both samples are generated for the same subjects under study. So, in this case, we need to use the paired-samples t-test or dependent samples t-test.

b. Do people own more pairs of workout shoes than dress shoes?

Answer: Two sample t test or independent samples t test

Explanation:

We are not given that the two samples are related or dependent. We have to check whether the average number of workout shoes is greater than the average number of dress shoes or not. So, we need to use two samples test for mean. We use independent samples t test because we are not given the values for the population standard deviations.

c. Is gender related to college major selection?

Answer: Chi-square test for independence

Explanation:

Here, we have to use chi square test for independence of two categorical variables.

Null hypothesis: H0: Two categorical variables gender and college major selection are independent.

Alternative hypothesis: Ha: Two categorical variables gender and college major selection are dependent.

Both variables are categorical and we have to check whether they are independent or not related.