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 sgnificance, test the claim that the amount contrbuted to the library fund is independent of ethnic group. Number of People Making Contribution $101-150 46 Ethnic Group S1-50 Over $200 20 25 28 31 104 $51-100 $151-200 Row Total 79 69 37 251 97 52 63 27 264 266 340 1121 83 60 58 37 99 85 266 53 72 239 Column Total 358 154 (a) What is the level of significance? State the null and alternate hypotheses. O Hg: Contribution level and ethnic group are not independent. H: Contribution level and ethnic group are independent. O Hg: Contribution level and ethnic group are independent. H: Contribution level and ethnic group are independent. O Hg: Contribution level and ethnic group are not independent. H: Contribution level and ethnic group are not independent. O Hg: Contribution level and ethnic group are independent. H: Contribution level and ethnic group are not 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 57 O Yes O No What sampling distribution will you use? O uniform O binomial O Student's t O hi-square O normal What are the degrees of freedom? (c) Find or estimate the Pvalue of the sample test statistic. (Round your answer to three decimal places.) (4) Based on your answers in parts (a) to (c), will you reject or fail to reject the nul hypothesis of independence? O Since the Pvalue > a, we fal to reject the null hypothesis. O Snce the Pvalue > a, we reject the null hypothesis. O Since the Pvalue sa, we reject the null hypothesis. O Since the Pvalue sa, we fal to reject the null hypothesis. (e) Interpret your condusion in the context of the application. O At the 1% level of significance, there is sufficient evidence to condude that contribution level and ethnic group are not independent. O At the 1% level of significance, there is insufficent evidence to conclude that contribution level and ethnic group are not independent.
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 sgnificance, test the claim that the amount contrbuted to the library fund is independent of ethnic group. Number of People Making Contribution $101-150 46 Ethnic Group S1-50 Over $200 20 25 28 31 104 $51-100 $151-200 Row Total 79 69 37 251 97 52 63 27 264 266 340 1121 83 60 58 37 99 85 266 53 72 239 Column Total 358 154 (a) What is the level of significance? State the null and alternate hypotheses. O Hg: Contribution level and ethnic group are not independent. H: Contribution level and ethnic group are independent. O Hg: Contribution level and ethnic group are independent. H: Contribution level and ethnic group are independent. O Hg: Contribution level and ethnic group are not independent. H: Contribution level and ethnic group are not independent. O Hg: Contribution level and ethnic group are independent. H: Contribution level and ethnic group are not 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 57 O Yes O No What sampling distribution will you use? O uniform O binomial O Student's t O hi-square O normal What are the degrees of freedom? (c) Find or estimate the Pvalue of the sample test statistic. (Round your answer to three decimal places.) (4) Based on your answers in parts (a) to (c), will you reject or fail to reject the nul hypothesis of independence? O Since the Pvalue > a, we fal to reject the null hypothesis. O Snce the Pvalue > a, we reject the null hypothesis. O Since the Pvalue sa, we reject the null hypothesis. O Since the Pvalue sa, we fal to reject the null hypothesis. (e) Interpret your condusion in the context of the application. O At the 1% level of significance, there is sufficient evidence to condude that contribution level and ethnic group are not independent. O At the 1% level of significance, there is insufficent evidence to conclude that contribution level and ethnic group are not independent.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text: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
$51-100
Ethnic Group 1-50
$101-150
$151-200
Over $200
Row Total
79
97
69
46
37
20
251
27
52
63
25
264
83
60
58
37
28
266
D
99
85
72
53
31
340
Column Total
358
266
239
154
104
1121
(a) What is the level of significance?
State the null and alternate hypotheses.
O Hg: Contribution level and ethnic group are not independent.
H: Contribution level and ethnic group are independent.
O Hg: Contribution level and ethnic group are independent.
H: Contribution level and ethnic group are independent.
O Hg: Contribution level and ethnic group are not independent.
H: Contribution level and ethnic group are not independent.
O Hg: Contribution level and ethnic group are independent.
H: Contribution level and ethnic group are not 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 57
O Yes
O No
What sampling distribution will you use?
O uniform
O binomial
O Student's t
O hi-square
O normal
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.)
(d) Based on your answers in parts (a) to (c), will you reject or fall to reject the null hypothesis of independence?
O Since the P-value > a, we fall to reject the null hypothesis.
O Since the P-value > a, we reject the null hypothesis.
O 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 condlusion in the context af the application.
O At the 1% level of significance, there is sufficient evidence to condlude 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.
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