The standard recommendation for automobile oil changes is once every 3000 miles. A local mechanic is interested in determining whether people who drive more expensive cars are more likely to follow the recommendation. Independent random samples of 48 customers who drive luxury cars and 39 customers who drive compact lower-price cars were selected. The average distance driven between oil changes was 3181 miles for the luxury car owners and 3218 miles for the compact lower-price cars. The sample standard deviations were 42.30 and 50.60 miles for the luxury and compact groups, respectively. Assume that the population distributions of the distances between oil changes have the same standard deviation for the two populations. Construct a 95% confidence interval for the difference in the mean distances between oil changes for all luxury cars and all compact lower-price cars. Let μ1 be the mean distance between oil changes for all luxury cars and μ2 be the mean for distance between oil changes for all compact lower-price cars.   Round your answers to two decimal places.

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.