Question

1. The scores of a physics test of a random sample of students (n = 8) are listed below. Is the sample significantly different from m = 65?
   1. State the null and alternative hypotheses
   2. Set the criteria for a decision: two-tailed test with a = .05
   3. Compute the test statistic using SPSS
   4. What is the effect size (you will need to compute Cohen’s d from data given in the SPSS output table)

d= M- μ / (SD)

5. (5 pts) Write the Results section for your findings. Include the descriptive statistics, type of statistical test and results of the test, effect size, Cohen’s d, and the confidence interval. Use the example I’ve given you.

Physics test scores (each cell is an individual score)

60	70
62	72
67	75
69	78

Answer 1

a) H0: the sample is not significantly different from mu = 65

H1: The sample is significantly different from mu = 65

b) Reject H0 if t value is not in Critical t values   ±2.3646

i.e. reject H0 if t value is < -2.3646 or reject H0 if t value > 2.3646

c) SPSS output:

Test statistic t = 1.911

d) The effect size (you will need to compute Cohen’s d from data given in the SPSS output table)

d= M- μ / (SD) = (69.13 - 65) / 6.105 = 0.676

e) From the output,

Sample Mean = 69.13

Sample SD = 6.105

Test statistic  t = 1.911

P-value = 0.098 which is > alpha 0.05 so we accept H0

Thus we conclude that  the sample is not significantly different from mu = 65

The 95% confidence interval for mu is (-0.98 , 9.23)

The constant Zero is contained in the above interval so we accept H0

Thus we conclude that  the sample is not significantly different from mu = 65

Cohen's d = 0.676 which is > 0.5 so it is medium effect