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 7% margin of error at a 90%
confidence level, what size of sample is needed?

Answer #1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 7% = 0.07

At 90% confidence level

= 1 - 90%

= 1 - 0.90 =0.10

/2
= 0.05

Z/2
= Z_{0.05 = 1.645} ( Using z table )

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

= (1.645 / 0.07)^{2} * 0.5 * 0.5

=138.0625

Sample size = 138

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?
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If the candidate only wants a 7% margin of error at a 99%
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