Question

A recent study of 34 gas stations in a large city revealed the mean price of unleaded gas was $0.87 per litre, with a population standard deviation of $0.02 per litre. Construct the 90% confidence interval for the population mean. Type your final answer, rounded to two decimal places, into the second blank, and the unit into the first blank. Answer: Between and .

Answer 1

Given a recent study of n = 34 gas stations in a large city revealed the mean price of unleaded gas was M = $0.87 per litre, with a population standard deviation of = $0.02 per litre. Now the confidence interval is calculated as:

μ = M ± Z(s_M)

where:

M = sample mean

= Population standard deviation
Z = Z statistic determined by confidence level
s_M = standard error = √(²/n)

Now the confidence interval is calculated as:

M = 0.87
Z = 1.645 Computed using the excel formula =NORM.S.INV(1-0.10/2)
s_M = √(0.02²/34) = 0

μ = M ± Z(s_M)
μ = 0.87 ± 1.645*0.0034
μ = 0.87 ± 0.0056

Thus the confidence interval of the population mean at 90% confidence level is between $ 0.86 and $ 0.88.