a- An automobile dealer wants to estimate the proportion of customers who still

Question

a- An automobile dealer wants to estimate the proportion of customers who still 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 hasbeen. 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. 2.0227 for 39 degree of freedom).

Explanation / Answer

a) here sample proportion phat =88/200 =0.44

for n=200 ; std error =(p(1-p)/n)1/2 =0.0351

from normal distribution for 95% confidence interval ;z= 1.96

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

b)

here std error of mean =-std deviation/(n)1/2 =5.8/(40)1/2 =0.917

for 95% CI and (n-1=39) degree of freedom ; critical value of t =2.0227

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

please revert for any clarification.

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