Question

Professor X is trying to raise people’s scores on the Smiley Face Test. He has 3 different experiments in the works and hopes that one of them will be effective. He has set the alpha for each experiment at .05. Each test will be two-tailed, which means his cutoff will be ± 1.96. Do step 4 for each of the following 3 experiments. Assume that the distribution of scores on the SFT for all the people in the population is normal, has a mean of 80, and has a standard deviation of 10

Prof. X’s first sample has a M = 76 and n = 25.

a) What would the Z score of this sample be on the comparison distribution?

b) What was the outcome of Professor X's first attempt at manipulating student scores.

What would the Z score of this sample be on the comparison distribution?

c) Prof. X’s second sample has a M = 82 and n = 25.

d) Prof. X’s third sample has a M = 84 and n = 20.

Answer 1

a)

here as z score =(M-mean)*sqrt(n)/std deviation

hence  Z score of this sample=(76-80)*sqrt(25)/10=-2

b) as this score is outside the limit of -/+1.96 ; this is effective,

c)

z score of second sample =(82-80)*sqrt(25)/10 =1

d)

z score of third sample =(84-80)*sqrt(20)/10 =1.79