We got some interesting results from a randomized experiment in a Stat 100 survey a few years ago.

People were randomly assigned to take 2 different versions of the survey. Everyone's questions were worded the same, the only difference was which picture accompanied their questions. For example, the quesion:

Are you in favor of the death penalty for a person convicted of murder?was either accompanied by the picture on the left or the picture on the right below:

219 people randomly got the version with the young guy and 323 randomly got the version with the menacing guy.

People were given the following response options:

1)Strongly Favor2)Favor3)Unsure4)Oppose5)Strongly Oppose.

We assigned a number to each response as shown above (1strongly favor >>>>>5strongly oppose.)

For each question the average and SD of students' responses are computed:

Death PenaltyAverageSDSample Size(n)Young Guy2.9221.249219Menacing Guy2.6041.164323

The question is: Is this observed differences between the 2 sample averages(that is, 2.922 - 2.604=0.318)small enough that it's likely to be due to the luck of the draw or is it too big to be due to chance and must reflect a real effect due to the images associated with the questions?

To make the significance test, pretend you have 2 independent random samples drawn from thousands of potential Stat 100 students who could have received the "young guy" version and all the thousands of potential Stat 100 students who could have received the "menacing guy" version and figure the SE's of the sample average.

In other words, the null hypothesis is that the images next to the question had no effect on the the responses.The averages inside the 2 boxes are theSAME. We just happened to randomly choose a group of students from the "menacing" box that happened to be more supportive of the death penalty. If we randomly drew a new batch of 219 and 323 from each box, the difference might disappear. The alternative hypothesis says: No, the average of the sweet looking guy box is > the average of the menacing looking guy and the difference in our sample averages reflects the real difference between the boxes; it reflects a real effect due to the images associated with the question. To make the significance test, pretend you have 2 independent random samples and figure the SE's.

1.Which of the following most accurately describes the null box(es)?

Remember the null hypothesis is always there is NO difference between the two groups in the larger population, the difference you see in the samples is just due to chance.

And the alternative is that there IS a difference between the two groups in the larger population. Those who are shown the more menacing guy do favor the death penalty more than those who are shown the sweet looking guy in the whole population and that's why we see such a difference in our sample.

There is one null box with 542 tickets. The average of the tickets is unknown but estimated from the sample.

There are 2 null boxes, one with 219 tickets and the other with 323 tickets. One box has an average of 2.922 and the other has an average of 2.604

There are 2 null boxes, each with thousands of tickets. One box has an average of 2.922 and the other has an average of 2.604

There are 2 null boxes, each with thousands of tickets. Both boxes have the same average.

Tries 0/22.The draws are made _______ replacement.

with

without

Tries 0/1

3.In the "young guy" group the SE of the average is (Round to 4 decimal places.)

Tries 0/34.In the "menacing guy" group the SE of the average is (Round to 4 decimal places.)

Tries 0/35.The difference between the 2 averages is 2.922-2.604=0.318; what is the SE of this difference? (Use your previously rounded answers for the SE's given above, and round the SE for the difference to 4 decimal places.)

Tries 0/36.What is the value of the test statistic z? ( Round to one decimal place, and use previously rounded answer)

Tries 0/3

7.What is the p-value? (Do not round the middle area. Do not round your answer. Use the previously rounded Z score above.)Click here to view the normal table

%

Tries 0/38.What do you conclude?

We cannot reject the null. It looks like the difference in averages could plausibly be due to chance

Reject the null, there is strong evidence that the associated images affect the responses.