For a sample of 100 honors students at a particular college, a sociologist collected the following...

For a sample of 100 honors students at a particular college, a sociologist collected the following information on the year of school and the willingness to help the school raise donations by making telephone calls to alumni:

Willingness To Help	Year in College
Willingness To Help	Freshman	Sophomore	Junior	Senior
Willing	15	16	15	15
Unwilling	15	14	5	5

Using these data, test the null hypothesis that willingness to help raise donations does not differ by year in school. Use a .05 confidence level for your test and be sure to report (a) the critical value of the test statistic, (b) the obtained value of the test statistic, (c) your decision about the null hypothesis, and (d) an interpretation of the meaning of your decision.

Expert Solution

Step 1. We put the value in a table and add them up to give the row total and col total and the grand total. As shown below.
Step 2 . We divide each value in the table with the grand total to get the frequency precentage.

Step 3. We need to find the expected distribution which is done below.
Step 4. We find the chi stat using the formula given below.

We sum all the chi value and get 5.56 and
Using chi table we find pvalue for the df = 6,
pvalue = 0.13494

Hypothesis
H0 : Willingness to help and Year in college are independent of each other
H1 : Willingness to help and Year in college are not independent of each other

Since the pvalue is greater than 0.05, we fail to reject the null hypothesis.
We conclude Willingness to help and Year in college is independent of each other

orchestra answered 2 years ago

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