Question

A sample of freshmen takes a reading comprehension test and their scores are summarized below. If the mean for the general population on this test is μ = 12, can you conclude that this sample is significantly different from the population. Test with α = .05. Include an effect size measure you find appropriate and explain why you chose what you calculated - you determine the tail and why. (up to 8 points)

Sample Scores: 16, 8, 8, 6, 9, 11, 13, 9, 10

Answer 1

= 10

s = 3

H₀: = 12

H₁: 12

The test statistic t = ()/(s/)

                             = (10 - 12)/(3/)

                            = -2

At alpha = 0.05, the critical values are t_{0.025, 8} = +/- 2.306

Since the test statistic value is not less than the lower critical value (-2 > -2.306), so we should not reject the null hypothesis.

So we cannot conclude that this sample is significantly different from the population.

Effect size = ()/s

                = (10 - 12)/3 = -0.67