Stats module 3.6 practice

Explain what a theoretical t-distribution for a single sample t-test is in the context of this research question.

If I were to run a single samples t-test (comparing mean reduction in depressive symptoms for the 10 -week therapy with the mean reduction in depressive symptoms for traditional individual therapy (μ = 25 on the Beck Depression Inventory)) with the same sample sizes as this sample an infinite number of times, a t-distribution of single sample t-test values would form that is symmetric and centered around zero.

Describe where the null hypothesis fits within the t-distribution in the context of this research question?

The t value or statistic for the null hypothesis would be close to zero or near the center of the t-distribution (t = 0) or no difference between the mean reduction in depressive symptoms for the 10 -week therapy and the mean reduction in depressive symptoms for traditional individual therapy (μ = 25 on the Beck Depression Inventory).

Describe the Alpha values purpose within a theoretical t-distribution

The alpha value for a two-tailed t-test represents two points in the distribution's tail that differentiate 95% of t-values in the center from 5% in the tails (2.5% in each tail). If your t-value lands to the left or right of these two extreme points, we would reject the null hypothesis and say the means are too different from each other for this to have happened by chance, when the null hypothesis in reality is true

Describe the zone of rejection and the zone of fail to reject the null hypothesis in t-distribution and within the context of this research question

If your calculated t-value lands in the 95% zone you would fail to reject the null hypothesis meaning that there is NO significant DIFFERENCE between the mean reduction in depressive symptoms for the 10 -week therapy and the mean reduction in depressive symptoms for traditional individual therapy (μ = 25 on the Beck Depression Inventory).

If your calculated t-value lands in the 5% zone (the tails of the distribution) you would reject the null hypothesis, meaning that THERE IS A significant difference between the mean reduction in depressive symptoms for the 10 -week therapy and the mean reduction in depressive symptoms for traditional individual therapy (μ = 25 on the Beck Depression Inventory).

In conclusion, explain what the p value is in relation to the t-value or statistic within the context of this research question.

the p value tells you that if you were to run this single samples t-test an infinite number of times, the probability of obtaining that t-statistic of t = 3.480 or more extreme when the null hypothesis is true is p = .033.
Because this is less than our alpha (p = .05), we will reject the null hypothesis and claim that the mean reduction in depressive symptoms for the 10 -week therapy is significantly different than the mean reduction in depressive symptoms for traditional individual therapy (μ = 25 on the Beck Depression Inventory).

A reject the null response

The probability of obtaining a t-test of -7.291 or more extreme, when the null hypothesis is true is less than .001 or 1 time out of 1000. REJECT THE NULL

A failed to reject the null response

The probability of obtaining a t-test of -1.002 or more extreme, when the null hypothesis is true is less than .831 or 831 times out of 1000. FAIL TO REJECT THE NULL.