Final answer:
The margin of error for a 95% confidence interval for the given sample of Exxon customers is approximately 2.71 gallons, calculated using the t-distribution for a sample of size 18 with a known standard deviation.
Step-by-step explanation:
The student has asked about determining the margin of error for a 95% confidence interval given a random sample of Exxon customers who used an average of 16.1 gallons to fill their vehicle, with a sample standard deviation of 5.4 gallons and a sample size of 18.
To calculate the margin of error, we need to use the t-distribution since the population standard deviation is not known and the sample size is less than 30. The margin of error (ME) is found using the formula ME = t*(s/√n), where t is the t-score corresponding to the desired confidence level and degrees of freedom (n-1), s is the sample standard deviation, and n is the sample size.
First, we will identify the t-score for a 95% confidence level with 17 degrees of freedom (n-1 = 18-1). Looking up the t-score in the t-distribution table we get approximately 2.11. Thus, the margin of error is:
ME = 2.11 * (5.4/√18) ≈ 2.71 gallons.