HW10: Problem 4 Previous Problem List Next (1 point) 2.5758 An automobile manufa

Question

HW10: Problem 4 Previous Problem List Next (1 point) 2.5758 An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by the local dealer. The customer relations department will survey a random sample of customers and compute a 99% confidence interval for the proportion who are not satisfied. (a) Past studies suggest that this proportion will be about 0.16. Find the sample size error of the confidence interval is to be about 0.015 (You will need a critical value accurate to at least 4 decimal places,) Sample size: needed if the margin of the (b) Using the sample size above, when the sample is actually contacted, 14% of the sample say they are not satisfied. What is the margin of the error of the confidence interval? MoE: Note: You can earn partial credit on this problem

Explanation / Answer

Solution:

a) Given that E=0.015

z for 90% confidence = 2.58

p = 0.16
sample size = z2* p(1-p)/E2

= 2.582*0.16*0.84/0.0152
=3976.08

sample size=3977 (always round up answer to next greater integer)

b) Margin of Error moe = z * sqrt[p(1-p)/n]
= 2.58*sqrt(0.14*0.86/3977)
= 0.0142

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