A sample is selected from a population with µ = 50

A sample is selected from a population with µ = 50. After a treatment is administered to  the individuals in the sample, the mean is found to be M = 55 and the variance is s​ 2​  = 64. 
 

a. If the sample has ​ n ​  = 4 scores, then conduct a hypothesis test to evaluate the  significance of the treatment effect and calculate Cohen’s d to measure the size of  the treatment effect. Use a two­ tailed test with ​ α ​  = .05.  

b. If the sample has ​ n​  = 16 scores, then conduct a hypothesis test to evaluate the  significance of the treatment effect and calculate Cohen’s d to measure the size of  the treatment effect. Use a two ­tailed test with ​ α ​  = .05. 

c. Describe how increasing the size of the sample affects the likelihood of rejecting  the null hypothesis and the measure of effect size.

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