Does the color of a sign that asks someone to do something make a difference in a person’s obedience to that sign? This is what a student researcher investigated. There are double doors at the entrance of her college’s library. She put a sign in the door on the right as you exit the library. The sign read, USE OTHER DOOR with an arrow pointing to the door on the left. She counted students as they exited the library to see what proportion used the door on the left when the sign was printed on red paper, printed on yellow paper, and (as a control) no sign at all. A summary of the data gathered was: 

• No sign: 13 of 55 used the left door 

• Yellow sign: 14 of 54 used the left door 

• Red sign: 25 of 53 used the left door 

a. Those that didn’t use the left door, used the right door. Organize the data into a two-way table, with the explanatory variable as the columns and the response variable as the rows. 

b. What is the explanatory variable in this study? Is it categorical or quantitative? 

c. What is the response variable in this study? Is it categorical or quantitative? 

d. Write out the null and alternative hypotheses for this study. 

e. For each condition, calculate the conditional proportion of those that used the left door. Write these as decimals. 

f. Compute the Mean Group Diff. 

g. A null distribution was generated for this dataset and is shown. Based on this distribution along with the Mean Group Diff, what can you say about the value of the p-value?

h. What is your conclusion based on your estimate of the p-value?  

Transcribed Image Text:

0 0.060 0.120 0.180 Shuffled Mean Group Diffs 0.240