Determine Sample Size?

2016-03-31 9:15 pm

A local telecom service provider is interested in estimating the population proportion of Hong Kong people who use global internet roaming service during a vacation abroad.

i) A recent study shows that 35 percent of Hong Kong people use global internet roaming service during a vacation abroad. What sample size is needed to provide 99 percent confident that the point estimate is correct to within ± 0.03 of the population proportion?

ii) Without the information in a), what sample size is needed to provide 99 percent confident that the point estimate is correct to within ± 0.03 of the population proportion?

更新1:

I need the calculation steps , thank you very much~

回答 (1)

[匿名]

2016-04-01 12:54 am

✔ 最佳答案

Margin of error = Confidence coefficient*Standard error of p
Margin of error = 0.03
Confidence coefficiet is the critical value of z for 99% confidence level = 2.575
Standard error of p = sqrt [p*(1-p)/n]

i) p^ = 35% or 0.35
Therefore,
0.03 = 2.575*sqrt [0.35*0.65/n]
n = {2.575*sqrt [0.35*0.65] / 0.03}^2 = 1677
Required sample size = 1677

ii) p = 0.5 shall be considered when p^ value is NOT known because the standard error of p is maximum at that level.
Therefore,
0.03 = 2.575*sqrt [0.5*0.5/n]
n = {2.575*sqrt [0.5*0.5] / 0.03}^2 = 1842
Required sample size = 1842

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