Question

A sample is selected from a population with µ = 62. After a treatment is administered to the individuals in the sample, the mean is found to be M = 68 and the standard deviation is s = 12.

A. Assume the sample has n = 9 scores and compute a single sample t-test and the estimated Cohen's d effect size.  Based on your computed t test value, can you reject H₀ witha two-tailed test α = .05? Write the appropriate t critical value and your decision about H₀.

B. Assume the sample has n = 25 scores and compute a single sample t-test and the estimated Cohen's d effect size. Based on your computed t test value, can you reject H₀ witha two-tailed test α = .05? Write the appropriate t critical value and your decision about H₀.

C. Compare your answers to A & B (i.e., decision about H₀ and estimated Cohen's d) and describe how

increasing the size of the sample affected the likelihood of rejecting the H₀ and the size of estimated Cohen's d.

Answer 1

A) Null Hypothesis

Alternative Hypothesis

Under H0, the test statistic is

Degrees of freedom = n-1 = 9-1 = 8

The critical value of t for 8 df at 5% significance level is 2.306

Since t calculated is less than t tabulated, Fail to Reject H0.

Cohen's d :

Medium Effect

B)

Null Hypothesis

Alternative Hypothesis

Under H0, the test statistic is

Degrees of freedom = n-1 = 25-1 = 24

The critical value of t for 24 df at 5% significance level is 2.064

Since t calculated is greater than t tabulated, Reject H0.

Cohen's d :

Medium Effect

C) As the sample size increases the likelihood of rejecting the null hypothesis increases because as the sample size increses, the standard error decreases.

And the sample size does not affects the effect size. i.e. Cohen's d is not affected by the sample size.