Question

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	81	57	66	30	17	251
B	100	54	56	30	24	264
C	71	70	59	39	27	266
D	103	83	65	58	31	340
Column Total	355	264	246	157	99	1121

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.)

B. A sociologist is studying the age of the population in Blue Valley. Ten years ago, the population was such that 20% were under 20 years old, 14% were in the 20- to 35-year-old bracket, 33% were between 36 and 50, 23% were between 51 and 65, and 10% were over 65. A study done this year used a random sample of 210 residents. This sample is given below. At the 0.01 level of significance, has the age distribution of the population of Blue Valley changed?

Find the sample test statistic. (Round your answer to two decimal places.)
  

Under 20	20 - 35	36 - 50	51 - 65	Over 65
29	29	67	65	20

Answer 1

A)

H₀: The amount contributed to the library fund is independent of ethnic group.

H₁: The amount contributed to the library fund is dependent of ethnic group.

At 1% level of significance,do not reject H₀. Therefore,the amount contributed to the library fund is independent of ethnic group.

B)

H₀: The age distribution of the population of Blue Valley not changed.

H₁: The age distribution of the population of Blue Valley changed.

At the 0.01 level of significance,do not reject H₀. Therefore,the age distribution of the population of Blue Valley has not changed.