The Union representing the Bottle Blowers of America (BBA) is considering a prop

Question

The Union representing the Bottle Blowers of America (BBA) is considering a proposal to merge with the Teamsters Union. According to BBA union bylaws, at least three-fourths of the union membership must approve any merger. A random sample of 2,000 current BBA members reveals 1,600 plan to vote for the merger proposal.

What is the estimate of the population proportion?

Develop a 95% confidence interval for the population proportion.

Basing your decision on this sample information, cab you concluded that the necessary proportion of BBA members favor the merger? Why?

A student in public administration wants to determine the mean amount members of city councils in large cities earn per month as remuneration for being a council member. The error in estimating the mean is to be less than $100 with a 95% level of confidence. The student found a report by department of Labor that reported a standard deviation of $1000. What is the required sample size?

A study was done on the proportion of cities that have private refuse collectors. The student wants the margin of error to be within 0.10 of the population proportion, the desired level of confidence is 90%, and no estimate is available for the population proportion. What is the required sample size? (Hint: Since, no estimate is available for the population proportion, use 0.5].

Explanation / Answer

1)

a) population proportion = 1600/2000 = 0.8

b)

standard error = sqrt(0.8 * 0.2 /2000) = 0.008944

margin of error = 1.96 * 0.008944 = 0.01753

confidence interval is

[ 0.8 - 0.01753 , 0.8 + 0.01753] which is

[0.78247 , 0.81753]

yes, we can say that with 95% confidence that people favor the merger

2)

n = ( Z(alpha/2) * std/E)^2

= ( 1.96 * 1000/100)^2

= 384.16

= 384

3)

standard error = sqrt(0.5 * 0.5/n)

=>

margin of error = 0.1

=>

1.645 * sqrt(0.5 * 0.5 /n) = 0.1

=>

sample size n = 270.60

= 271

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