You MUST show all work (Including the formula you used, important statistics suc

Question

You MUST show all work (Including the formula you used, important statistics such as critical value, margin of error.)For Confidence Interval, you MUST write down your answer in this format: (Lower bound, Upper bound), like (2858.26, 3381.74).

In a random sample, 136 of 400 persons given a flu vaccine experienced some discomfort.

1) Set up a 95% confidence interval for the true proportion of people who will experience some discomfort.

2) Find the minimum sample size needed to estimate the population proportion p with 99% confidence. The estimate must be accurate to within 0.02 of p.

Explanation / Answer

here point estimate p=136/400 =0.34

and std error =(p(1-p)/n)1/2 =0.0237

also for 95% CI, z=1.96

hence confidence interval =point estimate -/+ z*Std error =.2936 ; 0.3864

2)for 99% CI, z=2.5758

marginj of error =0.02

as estimation not given ; p=0.5

hence sample size =(n(1-p)(Z/E)2 =~4147

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