Question

A sample is selected from a population with µ = 50. After treatment is administered, we find top enclose x = 55 and sigma2 = 64. a. Conduct a hypothesis test to evaluate the significance of the treatment effect if n = 4. Use a two-tailed test with α = .05. If it is significant, how large is the effect (Cohen’s d)? b. Keeping all else equal, re-evaluate the significance if the sample had n = 16 participants. If it is significant, how large is the effect (Cohen’s d)? Both parts of this question should include: (1) type of t-test, (2) df, (3) t-crit, (4) SE, (5) t-obt, (6) conclusion, (7) cohen's dz, (8) R2 c. Describe how increasing sample size affects the calculation, and ultimately, significance.

Answer #1

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

alpha=0.05

i) n=4

degrees of freedom= n-1=4-1=3

t critical= 3.18

Since t critical is greater than t cal therefore DO NOT reject null hypothesis H0.

Conclusion: We don't have sufficient evidence to conclude that population mean is different from 55.

Cohen's d=

R squared= (0.2983)^2= 0.08898289

ii) n=16

degrees of freedom= n-1=16-1=15

t critical= 2.13

Since t critical is SMALLER than t cal therefore reject null hypothesis H0.

Conclusion: We have sufficient evidence to conclude that population mean is different from 55.

Cohen's d= t/sqrt(N)= 5/8= 0.625

R squared= (0.2983)^2= 0.08898289

On increasing the sample size the test has become SIGNIFICANT.

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