In a recent sample of 84 used car sales costs, the sample mean was $6,425 with a standard deviation of $3,156. Assume the underlying distribution is approximately normal.
i. Construct a 95% confidence interval for the population mean cost of a used car.
ii. Calculate the error bound.
iii. Explain what a “95% confidence interval” means for this study.
i.
mean = 6425 n = 84 and standard deviation = 3156
The 95% confidence interval for the population mean is,
=mean ± 1.96 *σ /√n
= 6425 + 1.96 * 3156 /√84
= 6425 + 147.28√21
= 6425 + 674.922
= 7099.922
= 6425 - 1.96 * 3156 /√84
= 6425 - 147.28√21
= 6425 - 674.922
=5750.078
Answer: (5750.078, 7099.922)
ii.
=EBM=Zα/2*σ/√n
EBM = 1.96 * 3156 / √84
= 674.922
iii.
The 95% confidence interval means that you are 95% confident that the mean lie in the interval 5750.078 and 7099.922
