An automobile dealer \"wants to estimate the proportion of customers who still o

Question

An automobile dealer "wants to estimate the proportion of customers who still own the cars they purchased five years earlier. A random sample of 200 customers selected from the automobile dealer's records indicates that 82 still own cars that were purchased five years earlier. a. Set up a 95% confidence interval estimate of the population proportion of all customers who still own the cars five years after they were purchased. A political pollster would like to estimate the proportion of voters who will for the Democratic candidate in a presidential campaign. The pollster would like 90% confidence t5hat her prediction is correct to within = 04 of the true proportion. What sample size is needed ? A consumer group would like to estimate the average monthly electric bills for the month of July for one - family homes in a large city/. Based upon studies conducted in other cities the standard division is assume to be $25. The group would like to estimate the average bill for July to within = of the average with 99 % confidence. What sample size is needed

Explanation / Answer

5) n = 200 X = 82

95 % confidence interval

z = 1.96 for alpha = 0.05

p^ = X/n = 82/200 = 0.41

standard error = sqrt(p^q^/n) = sqrt(0.41*0.59/200) = 0.034777866

(p^ - z *s.e , p^ + z* s.e)

=(0.41 - 1.96*0.034777866), (0.41+1.96*0.034777866)

=(0.34183, 0.478164)

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