Question

Garrison Keller claims the children of Lake Wobegon are above average. You take a simple random sample of 9 children from Lake Wobegon and measure their intelligence with a Wechsler test and find the following scores: {116, 128, 125, 119, 89, 99, 105, 116, and 118}. The mean of this sample (? ̅) is 112.8. We know Wechsler scores are scaled to be normally distributed with a mean of 100 and standard deviation of 15. Is this sample mean sufficiently different from a population mean (µ) of 100 to reject the null hypothesis of “no difference?”

a. State your null and alternate hypothesis.

b. Test your hypothesis assuming level 0.05 as the level of significance.

c. Using the ‘p’ value approach to test the researchers claim about the children of Lake Wobegon.

Answer 1

a) Null: sample_mean = 100
Alternate: sample_mean != 100 (not equal to 100)

b) t = (112.8-100) / (15/sqrt(9)) = 2.56
degrees of freedom = n-2 = 7
significance level = 1-0.05/2 = 0.975 (two sided)
critical t value = 2.365
t statistic > critical t value, hence null is rejected

c) p-value = 0.037552
As p < 0.05 (significance level), the null maybe rejected