Question 3: a- An automobile dealer wants to estimate the proportion of customer

Question

Question 3: a- An automobile dealer wants to estimate the proportion of customers who stl own the cars they purchased six years ago. A random sample of 200 customers selected from the automobile dealer's records indicates that 88 still own cars that were purchased six years earlier. Construct a 95% confidence interval estimate of the population proportion of all customers who still own the cars they purchased six years ago b- A sample of 40 country CD recordings of Willie Nelson has been examined. The average playing time of these recordings is 51.3 minutes, and the standard deviation is 5.8 minutes. Construct a 95% confidence interval for the mean playing time of all Willie Nelson recordings. (t = 2.0227 for 39 degree of freedom)

Explanation / Answer

here estimated proportion p=88/200=0.44

std error =(p(1-p)/n)1/2 =0.0351

for 95% CI ; z =1.96

hence 95% confidence interval for population proportion =sample proportion -/+ z*Std error=0.3712 ; 0.5088

b)

std error of mean=std deviation/(n)1/2 =5.8/(40)1/2 =0.9171

for 95% confidence interval of mean =sample mean -/+ t*std error =49.4451 ; 53.1549

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