Answer Happy

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. Ethnic Group A B С D D Column Total $1-50 77 96 77 108 358 Number of People Making Contribution $51-100 $101-150 $151-200 Over $200 56 68 36 14 53 71 26 18 58 64 39 28 80 68 51 33 247 271 152 93 Row Total 251 264 266 340 1121 (a) What is the level of significance? 0.01 State the null and alternate hypotheses. O Ho: Contribution level and ethnic group are not independent. Hz: Contribution level and ethnic group are not independent. O Ho: Contribution level and ethnic group are independent. Hj: Contribution level and ethnic group are independent. O Ho: Contribution level and ethnic group are independent. Hz: Contribution level and ethnic group are not independent. O Ho: Contribution level and ethnic group are not independent. Hj: 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? O Yes Ο Νο

What sampling distribution will you use? O normal O binomial O uniform O Student's t O chi-square 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.) O p-value > 0.100 O 0.050 < p-value < 0.100 O 0.025 < p-value < 0.050 O 0.010 < p-value < 0.025 O 0.005 < p-value < 0.010 O 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? O Since the P-value > a, we fail to reject the null hypothesis. Since the P-value > a, we reject the null hypothesis. Since the P-value sa, we reject the null hypothesis. O Since the P-value sa, 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. O At the 1% level of significance, there is insufficient evidence to conclude that contribution level and ethnic group are not independent.