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 10 L. From his records, he selects a random sample of 14 sales and finds the mean number of litres sold is 44.

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 (mean or variance) would be included in about  intervals.

Answer 1

Population standard deviation

Sample size ,n = 14

Sample mean

(A) point estimate of population mean is sample mean .So point estimate of population mean = 44 litres.

(B) because sample size is small we use t distribution for 95% confidence interval and n-1= 14-1= 13 degree of freedom the value of t is 2.160.

So confidence interval for population mean is

  

Thus  

  

Thus 95% confidence interval for population mean is between 38.227 and 49.773

(C) this means that we are 95% confident that population mean is within (38.227,49.773) this interval.