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
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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