A researcher wanted to find out if there was difference between the estimates given for a female actor’s earnings and a male actor’s earnings. The researcher hypothesized that the estimates would be higher for a male actor than for a female actor. Based on data provided at www.boxofficemojo.com, the researcher identified Daniel Radcliffe as a top male money maker (average earnings per film = $155.1 million) and Jennifer Lawrence as a top female money maker (average earnings per film = $137.1 million). The researcher then asked a random sample of movie goers to give their best estimates of Daniel Radcliffe’s average earnings per film and Jennifer Lawrence’s average earnings per film. Carry out a directional Wilcoxon T Test for two related samples on the estimates to find out if the distributions are equal. Follow the steps given below the table and use a significance level of .05 for the directional test.

Estimate of Actors' Average Earnings Per Film

(in millions)

Daniel Radcliffe ........................................ Jennifer Lawrence
$1 .......................................................................... $1
$10 ..................................................................... $10
$15 ...................................................................... $80
$25 .................................................................... $100
$200 .................................................................... $10
$5 ....................................................................... $20
$100 ................................................................... $15
$10 ..................................................................... $60

a. Present the null hypothesis.

b. Present the alternative hypothesis.

c. Determine n, the number of nonzero difference scores.

d. Identify the critical value of T in Table F of your textbook.

e. Present the decision rule.

f. Calculate T.

g. Present a statistical decision.

h. Present a conclusion in the context of the research situation. You may assume that both populations have the same variability and the same shape.