A market research firm is hired to perform a survey and analyze the true proportion of...

A market research firm is hired to perform a survey and analyze the true proportion of the households with pets. How many households should they survey in order to be 90% confident that the estimated (sample) proportion is within two percentage points of the true population? Assume that pq = 0.25

Expert Solution

Solution :

Given that,

pq = 0.25

margin of error = E = 0.02

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

sample size = n = (Z / 2 / E )2 * pq

= (1.645 / 0.02)2 * 0.25

= 1691.27

sample size = 1692

orchestra answered 2 years ago

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