Question

A researcher wishes to estimate the number of days it takes an automobile dealer to sell a Ferrari 458. A random sample of 50 cars had a mean time on the dealer’s lot of 54 days. Assume the population standard deviation to be 6.0 days.

1. Find the best point estimate of the population mean.

DAYS. (Round answer to two decimal places)

2. Find the margin of error for the 95% confidence level.

DAYS. (Round answer to two decimal places)

3. Find the 95% confidence interval for the population mean. ((Round answer to two decimal places)

≤ µ ≤

4. What sample size is needed, at the 95% confidence level, to ensure an error of no more than 1 day?

n =   (must be a whole number)

Answer 1

n = 50

Sample mean =

Population standard deviation =

1) Best point estimate of the population mean is always a sample mean.

Best point estimate of the population mean is 54

2)

Confidence level = c = 0.95

Margin of error (e) :

Where zc is z critical value for (1+c)/2 = (1+0.95)/2 = 0.975

zc = 1.96

e = 1.66 (Round to 2 decimal)

Margin of error = 1.66

3)

95% confidence interval for the population mean is

(Round to 2 decimal)

95% confidence interval for the population mean is

4)

Confidence level = c = 0.95

zc is z critical value for (1+c)/2 = (1+0.95)/2 = 0.975

zc = 1.96

e = margin of error = 1

Sample size (n) :

n = 138 (Round to nearest whole number)

Sample size = 138