Question

A movie production company wishes to test whether three different endings of a soon-to-be released movie is associated with significantly different levels of recommendation. The production company designs an experiment where they randomly select California residents and then randomly assign them to view the movie with one of the three different endings. In the first ending the protagonist gets the girl; in the second ending the protagonist ends up with somebody prettier and nicer; in the third ending the protagonist ends up alone but realizes that the most important relationship she has is with herself end her transformative journey begins there at the ending! Out of the 36 participants who were randomly assigned to view the movie with first ending 21 said that they would recommend the movie; out of the 19 participants who were shown the second ending eight reported that they would recommend the movie; and out of the 22 participants who viewed the movie with the third ending 18 reported that they would recommend the movie.

State the value of the observed chi square score rounded to the nearest hundredth. Remark: rounding counts!

Answer 1

We have divided the viewers into subgroups of different endings. Then it is observed whether they would recommend the movie or not. So this is to test if the proportion / distribution is same or not for all the groups. For this we will use chi-square test of homogenity.

If out of the 36 participants who were randomly assigned to view the movie with first ending 21 said that they would recommend the movie then 15 (36-21) would not recommend. Similarly we find for others as well.

Ending	recommend
Yes	No	Total
1st	21	15	36
2nd	8	11	19
3rd	18	4	22
Total	47	30	77

These are the observed values. For the test statistics we also need the expected values

The expected value for each cell is found by =Row total * col total/ overall total

Expected
Ending	recommend
Yes	No	Total
1st	21.974	14.026	36
2nd	11.597	7.403	19
3rd	13.429	8.571	22
Total	47	30	77

(O; - E;) E	recommend
Ending	Yes	No
1st	0.043	0.068
2nd	1.116	1.748
3rd	1.556	2.438

Chi -square test STat =

(0; – E;) Ei

Test Stat = 6.969 = 6.97