Question

An estimate is needed of the mean acreage of farms in a certain city. A​ 95%...

An estimate is needed of the mean acreage of farms in a certain city. A​ 95% confidence interval should have a margin of error of

22 acres. A study ten years ago in this city had a sample standard deviation of 210 acres for farm size.

acres for farm size. Answer parts ​(a​) and ​(b​).

a. About how large a sample of farms is​ needed?

n=? ​(Round up to the nearest​ integer.)

b. A sample is selected of the size found in​ (a). However, the sample has a standard deviation of 280 acres rather than 210.

What is the margin of error for a​ 95% confidence interval for the mean acreage of​ farms?

m=? ​(Round to one decimal place as​ needed.)

Homework Answers

Answer #1

a).given data are:-

margin of error (E) = 22

z critical value for 95% confidence level, both tailled test be:-

the needed sample size be:-

b).given data are:-

sample size (n) = 351

[ as n = 351 >30, we can using approximation ]

the margin of error for a​ 95% confidence interval for the mean acreage of​ farms be:-

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