A researcher wishes to estimate, with 9090% confidence, the proportion of adults who have high-speed Internet access. Her estimate must be accurate within 55% of the true proportion. a) Find the minimum sample size needed, using a prior study that found that 2828% of the respondents said they have high-speed Internet access. b) No preliminary estimate is available. Find the minimum sample size needed.

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JeanaShupp JeanaShupp · Answer 1 · 2019-11-01T05:02:44+01:00

Answer: a) Required minimum sample size= 219

b) Required minimum sample size= 271

Step-by-step explanation:

As per given , we have

Margin of error : E= 5% =0.05

Critical z-value for 90% confidence interval : [tex]z_{\alpha/2}=1.645[/tex]

a) Prior estimate of true proportion: p=28%=0.28

Formula to find the sample size :-

[tex]n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.28(1-0.28)(\dfrac{1.645}{0.05})^2\\\\=218.213856\approx219[/tex]

Required minimum sample size= 219

b) If no estimate of true proportion is given , then we assume p= 0.5

Formula to find the sample size :-

[tex]n=0.5(1-0.5)(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.25(\dfrac{1.645}{0.05})^2\\\\=270.6025\approx271[/tex]

Required minimum sample size= 271