Question

.Researchers studied the effects of electrical stimulation near the parietal lobe on math skills. They took at sample of n=25 students who received electrical current for 30 minutes a day. For the general population the performance on math was u 80 and 20. If you sample obtains M-87. You are sure that the math skills will improve. Conduct a 1-tailed test at a = .05 Show all four steps! a. b. For the question above, calculate the effect size, Cohen's d. How do you interpret the effect size?

Answer 1

i) To test
Ho: 80
against $H_1:\mu > 80$

ii) The test statistic can be written as

which under H₀ follows a standard normal distribution.

νη (M-80) σ

We reject H₀ at 0.05 level of significance if P-value < 0.05

Now,

The value of the test statistic =

obs= 1.75

iii) P-value

P(Z obs) P(Z > 1.75) =1 - P(Z<1.75) 1 0.959941 0.040059

iv) Conclusion : Since P-value < 0.05, so we reject H₀ at 0.05 level of significance and we can conclude that math score has been significantly increased.

b) Cohen's d

87-80 = 0.35 20

Since d = 0.35, there is medium effect of treatment on math score.