Question

A report states that 44% of home owners had a vegetable garden. How large a sample...

A report states that 44% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 6% with 95% confidence?

A. 132

B. 66

C. 263

D. 526

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Solution :

Given,

E = 6% = 0.06

c = 95% = 0.95

or p = 44% = 0.44

1 - 1- p = 1 - 0.44 = 0.56

Now,

= 1 - c = 1 - 0.95 = 0.05

/2 = 0.025

= 1.96 ......(using z table)

The sample size for estimating the proportion is given by

n =

= (1.96)2 * 0.44 * 0.56 / (0.062)

= 262.93617

= 263 ..(round to the next whole number)

Answer : Option C is correct

Required Sample size is n = 263

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