After a large fund drive to help the Boston City Library, the following information was obtained from a random sample of contributors to the library fund. Using a 1% level of significance, test the claim that the amount contributed to the library fund is independent of ethnic group.

Number of People Making Contribution
Ethnic Group $1-50 $51-100 $101-150 $151-200 Over $200 Row Total
A 77 63 54 39 18 251
B 90 48 76 26 24 264
C 73 67 59 37 30 266
D 108 82 70 50 30 340
Column Total 348 260 259 152 102 1121

(a) What is the level of significance?

State the null and alternate hypotheses.

H0: Contribution level and ethnic group are not independent.
H1: Contribution level and ethnic group are independent. H0: Contribution level and ethnic group are not independent.
H1: Contribution level and ethnic group are not independent. H0: Contribution level and ethnic group are independent.
H1: Contribution level and ethnic group are not independent. H0: Contribution level and ethnic group are independent.
H1: Contribution level and ethnic group are independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

Yes No

What sampling distribution will you use?

normal uniform Student's t chi-square binomial

What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.005 < p-value < 0.010 p-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis. Since the P-value > α, we reject the null hypothesis. Since the P-value ≤ α, we reject the null hypothesis. Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 1% level of significance, there is sufficient evidence to conclude that contribution level and ethnic group are not independent. At the 1% level of significance, there is insufficient evidence to conclude that contribution level and ethnic group are not independent.