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7 February, 10:26

A 2005 poll reported that 78 % of people worried that they would be exposed to SARS. Find the approximate margin of error if (a) nequals119 , (b) nequals314 , (c) nequals1993. Explain how the margin of error changes as n increases.

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  1. 7 February, 12:11
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    (a) Margin of error = 0.038

    (b) Margin of error = 0.023

    (c) Margin of error = 0.0093

    The margin of error decreases as n increases

    Explanation:

    Margin of error (E) = sqrt[p (1-p) : n]

    p is the population proportion = 0.78

    n is sample size

    (a) n = 119

    E = sqrt[0.78 (1 - 0.78) : 119] = sqrt[1.442*10^-3] = 0.038

    (b) n = 314

    E = sqrt[0.78 (1 - 0.78) : 314] = sqrt[5.465*10^-4] = 0.024

    (c) n = 1993

    E = sqrt[0.78 (1 - 0.78) : 1993] = sqrt[8.610*10^-5] = 0.0093

    The margin error decreases as n increases because the relationship between E and n is inverse in which an increase in one quantity (n) leads to a corresponding decrease in other quantity (E)
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