Each year, the US Environmental Protection Agency (EPA) releases fuel economy data on cars manufactured in that year. Below are summary statistics on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions manufactured in 2012. Do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage? Assume that conditions for inference are satisfied.
Automatic: mean = 16.12, standard deviation = 3.58, n = 26
Manual: mean = 19.85, standard deviation = 4.51, n = 26The t-distribution was invented by William S. Gosset to use in those scenarios where the z-distribution cannot be used. But there are some assumptions to use the t-distribution like:
The sample should be random.
The sampling distribution should be approximately normal.
There should not be an outlier in the data set.
The data values are independent of each other.
