Question

In: Statistics and Probability

How to do a dependent sample t-test and find t-crit

Expert Solution

Procedure for dependent sample t - test and find t - crit:

Step 1:

Null Hypothesis H0 assumes the true mean difference ( ) is equal to zero.

The two - tailed Alternative Hypothesis (H1) assumes that is equal to zero.

The upper - tailed Alternative Hypothesis (H1) assumes that is greater than zero.

The lower - tailed Alternative Hypothesis (H1) assumes that is less than zero.

Step 2:

Calculate Sample mean () from the sample data of the differences.

Step 3:

Calculate Sample Standard Deviation (s_d ) from the sample data of the differences.

Step 4:

Calculate Standard Error (SE):

Step 5:

Calculate the Test Statistic:

Step 6:

Calculate the probability of observing the test statistic under the null hypothesis. This value is obtained by comparing t to a t - distribution with n - 1 degrees of freedom.This is done by looking up the value in t Table.

Step 7:
If the calculated value of t is greater than critical value of t, the difference is significant. Reject null hypothesis. Conclusion: The data support the claim that the mean difference is not zero.

If the calculated value of t is less than critical value of t, the difference is not significant. Fail to reject null hypothesis. Conclusion: The data do not support the claim that the mean difference is not zero.

orchestra answered 2 years ago

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