Question

FOR THE SCENARIO BELOW...I need to know if my hypotheses are directional or non-directional.(I already have the hypotheses)

I know I need to use a two sample T test but need help with the calculations. (Provide a sample size and critical values in relation to the hypothesis.)

-Discuss what the statistical analysis will do in answering the hypotheses and question(s) for the client. Also discuss any potential problems to watch out for, including an appropriate sample size to meet the assumptions of the statistical test.

Client Scenario: Jackson Hole Mind and Body Works

My name is Jane, and I am a licensed counselor who owns a business in Jackson Hole, Wyoming. This past year, I started a couple laughing yoga classes that combine the anxiety removing benefits of yoga with the emotional release of laughter. It has been a lot of fun and many clients love it, but a competitor has been criticizing my new approach as a sham and quackery. I am confident that my laughing yoga classes are beneficial, but I would like you to perform a study that examines the impact of my approaches from a scientific perspective. I know that science needs to be objective, so I would like you to setup a study for me as a nonbiased researcher. My thoughts are that I could give you the email addresses of clients who are willing to be in the study, and you would ask each of them questions, and then analyze the results.

            I would like you to examine two types of therapy I conduct, my laughing yoga therapy and my more traditional cognitive behavioral therapy.   I expect that 40 participants will be available from my laughing yoga classes, and that 50 participants will be available from my traditional cognitive behavioral therapy sessions. It would be nice if you asked questions related to clients’ current healthy living practices and use of positive emotions. You can determine the exact questions to ask clients. I was thinking that I would offer each participant in the study a couple free smoothie drinks at a local juice bar for participating in the research.

Answer 1

This is a non-directional alternate hypothesis.

Since the client is saying that they expect that 40 participants will be available from laughing yoga classes and that 50 participants will be available from my traditional cognitive behavioural therapy sessions. You could take 40 participants from each class.

The sample size is large enough for you to use t-test because you don' have a population standard deviation, otherwise, z-test would have been used.

The t-critical values for a two-tailed test, for a significance level of α=0.05 and df =40-1=39, are

The formula for a t-statistic for two population means (with two independent samples), with unknown population variances depends on whether the population variances are assumed to be equal or not. If the population variances are assumed to be unequal, then the formula is:

On the other hand, if the population variances are assumed to be equal, then the formula is:

Normally, the way of knowing whether the population variances must be assumed to be equal or unequal is by using an F-test for equality of variances.