Question

"Snoqualmie" is a name shared by a waterfall and a tribe of Native Americans. In a study of the cultural importance of the waterfall, two groups of the Snoqualmie tribe were randomly surveyed. One group consisted of Snoqualmie members living less than 25 miles from the waterfall. Another group consisted of Snoqualmie members living more than 25 miles from the waterfall. The researchers asked each member to rate the cultural importance of the waterfall as low, medium, or high. Data from the study are presented in the following table.

Members Living More Than 25 Miles from the Waterfall Members Living Less Than 25 Miles from the Waterfall Total
Low 25 17 42
Medium 8 21 29
High 5 12 17
Total 38 50 88

Required:
If the distributions of ratings are the same for those Snoqualmie members living less than 25 miles from the waterfall and those living more than 25 miles from the waterfall, what is equal to the expected count of members living less than 25 miles from the waterfall who rated the cultural importance as high?

Answer 1

Expected count frequency= 17*50/88= 9.659

Explanation:

Members Living More Members Living Less Total

Than 25 Miles Than 25 Miles

from the Waterfall from the Waterfall

Low 25 17 42

Medium 8 21 29

High 5 12 17

Total 38 50 88

We see that the total of the high row is 17 and the total of the members living less than 25 miles from the waterfall is 50 .

So using the formula :

Expected count frequency= row total * column total/ grand total

= 17*50/88= 9.659

All the expected frequencies can be found in a similar way and then compared to the observed frequency to test the chi square.