Part I. Formulas and Procedures. Compute each of the following using the correct

Question

Part I. Formulas and Procedures. Compute each of the following using the correct formulas and procedures. All steps and all work must be shown to receive full credit. Proper units must be given with answer, write all formulas used for each problem. Find and identify pa, x, n,, /2, z a (critical value) and E where needed. Read individual instructions carefully. 1. Fifty people are selected randomly from a certain population and it is found that 12 people in the sample are over 6 feet tall. What is the point estimate of the proportion of people in the population who are over 6 feet tall? What proportion of people in the population is not over 6 ft tall? (6 pts) 2. Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round point estimate to two decimal places. Round the margin of error to four decimal places. (8 pts) 95% confidence; n = 2388, x-1672 3. Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. (8 pts) 90% confidence; the sample size is 800, of which 40% are successes

Explanation / Answer

Solution:-

1) =>  That is the point estimate of the proportion over 6 feet tall = 12/50 =  0.24

=>  That is the point estimate of the proportion not over 6 feet tall = 1-0.24 = 0.76

2) n = 2388 , x = 1672 , 95% confidence = 1.96

p = X/n = 1672/2388 = 0.70 , q = 1 - p = 0.30

ME = z*sqrt[p*q/n]

ME = 1.96*sqrt[0.70*0.30/2388] = 0.0184

3) n = 800 , p = 0.40 , q = 1 - p = 0.60 , 90% confidence = 1.645

   ME = z*sqrt[p*q/n]

ME = 1.645*sqrt[0.40*0.60/800] = 0.0285

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