Question

1. 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 s²= 64.

For a sample of n = 16 scores, conduct a single sample t-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. Show the sampling distribution. dont forget to show the smapling distibution(2 pts)

Answer 1

Solution :

Given that,

= 55

s2 = 64

s = 8

n = 16

a.) Hypothesis:

H0 : 50

Ha : 50

Test Statistic:

t = ( - ) / (s /n)

t = (55 - 50 ) / ( 8 / 16 )

t = 2.5

P - value = 0.0245

if P- value < =0.05 then reject H0.

P-value < 0.05, we reject H0.