Question

Bob Nale is the owner of Nale's Texaco GasTown. Bob would like to estimate the mean number of litres (L) of gasoline sold to his customers. Assume the number of litres sold follows the normal distribution with a standard deviation of 12 L. From his records, he selects a random sample of 15 sales and finds the mean number of litres sold is 47.

a. What is the point estimate of the population mean? (Round the final answer to the nearest whole number.)

The point estimate of the population mean is            litres.

b. Develop a 95% confidence interval for the population mean. (Round the final answers to 3 decimal places.)

The 95% confidence interval for the population mean is between  and  .

c. Interpret the meaning of part (b).

If 100 such intervals were determined, the population  (Click to select)  variance  mean  would be included in about  intervals.

Answer 1

a)

Point estimate = sample mean, xbar = 47

b)

sample standard deviation, σ = 12
sample size, n = 15

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

ME = zc * σ/sqrt(n)
ME = 1.96 * 12/sqrt(15)
ME = 6.07

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (47 - 1.96 * 12/sqrt(15) , 47 + 1.96 * 12/sqrt(15))
CI = (40.927 , 53.073)

c)

If 100 such intervals were determined, the population mean would be included in about intervals.