You want to estimate the average gas price in your city for a litre of regular unleaded gasoline.You take a random sample of prices from 15 gas stations,recording an average cost of $1.27 and a standard deviation of $0.06.Create a 95% confidence interval for the mean price per litre of gas.

Question

Quizplus · Accepted Answer

To create a 95% confidence interval, we need to use a t-distribution with 14 degrees of freedom (n-1=15-1=14) since we don't know the population standard deviation. Using a t-distribution table, we find the t-value to be 2.145.

The formula for a confidence interval is: 
(sample mean) +/- (critical value) x (standard error)
where the standard error is the standard deviation divided by the square root of the sample size.

Plugging in our values:
(sample mean) +/- (2.145) x (0.06/sqrt(15))

Calculating:
1.27 +/- 0.054

So the confidence interval is ($1.24, $1.30).

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