Question

A political candidate has asked you to conduct a poll to
determine what percentage of people support her.

If the candidate only wants a 10% margin of error at a 90%
confidence level, what size of sample is needed?

Give your answer in whole people

Answer #1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 10% = 0.10

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_{/2}
= Z_{0.05} = 1.645

Sample size = n = (Z_{/2}
/ E)^{2} *
* (1 -
)

= (1.645 / 0.10)^{2} * 0.5 * 0.5

= 67.65

Sample size = 68

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