A web based software company is interested in estimating theproportion of indivi

Question

A web based software company is interested in estimating theproportion of individuals who use the Firefox browser. In a sampleof 200 of individuals, 35 users stated that they used Firefox.Using this data, construct a 99% confidence interval for theproportion of all individuals that use Firefox.
1.What is the lower limit on the 99% confidence interval? Give youranswer to three decimal places.

2.What is the upper limit on the 99% confidence interval? Give youranswer to three decimal places.

3.Google states that the proportion of all individuals that useFirefox is 0.2. Based on the interval above, does the Google claimseem reasonable?
1 No because 0.2 is not inside theinterval. 2.No because 0.2 isinside the interval. 3. Yesbecause 0.2 is inside the interval. 4. Yes because 0.2 is not inside the interval.

4.What sample size would be required so that the width of the 99%confidence interval would be at most 0.04 units wide? Be asconservative as possible with your answer!

Explanation / Answer

background information n=200 n=200=14.142 probability of users using Firefox=p=35/200=0.175 probability of users not using Firefox=q=165/200=0.825 mean=expected value=np=200*0.175=35 =npq=200*0.175*0.825=5.373 99% CI=(mean±2.575*/n) =35±2.575*(5.373/14.142) =35±0.978 =(34.022,35.978) 1).lower limit on the 99% confidence interval=34.0 2).upper limit on the 99% confidence interval=35.978 3).Google states that the proportion of all individuals that useFirefox is 0.2. this mean every 200 user, we would expect 200*0.2=40 if them areusing Firefox Based on the interval above, 1 No because 0.2 is not inside theinterval.

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