Question

We know that pain ratings from the Cruciatus curse are normally distributed in the population with a mean of 6.3 and a standard deviation of 1.6. Hermione’s sample of 100 subjects rated their pain as 5.2.

a) What is the mean of the comparison distribution?

b) What is the standard deviation of her comparison distribution? (Hint: You'll need to calculate the sampling distribution of the mean).

c) Convert the mean of Hermione’s sample to a Z score in the comparison distribution.

d) If Hermione set her alpha to .05 and did a one-tailed test, then what would be her cutoff on the comparison distribution?

e) What should Hermione do based on her Z-test?

Answer 1

here population mean for pain ratings for the Cruciatus curse = 6.3

standard deviation for pain ratings for the Cruciatus curse = 1.6

sample size mean = 5.2

(a) Here the mean of the comparison distrivution = 5.2

(b) Standard deviation of her comaprison distribution = 1.6/sqrt(100) = 0.16

(c) Z = (5.2 - 6.3)/0.16 = -6.875

(d) Here alpha = 0.05 and one tailed test

critical value of test statisric = 1.645

then her cutoff on the comparison distribution, then the cutoff is < 6.3 - 1.645 * 0.16

< 6.037

(e) Here based on her Z - test, we will see that the pain ratings will reduce.