An internal report issued by the marketing manager of a oil-change franchise claims that the mean number of miles between oil changes is for franchise customers is at least 3600 miles. One franchise owner suspects that the mean distance is actually less than 3600 miles. She collects a random sample of 10 customers, and determines the distance each had driven between oil changes. She finds the following results.
3655 3734 3700 1946 3208
3311 2789 3920 3555 3902
a) Construct a stem-and-leaf diagram.
b) Does your stem-and-leaf diagram in (a) suggest that the distribution of distances is not normal? (For instance, is there any evidence that the distribution is skewed?)
c) Construct TWO 99% confidence intervals.
(i) Use the z-tables.
(ii) Use the t-tables.
d) Interpret your result in (ii) in words.
e) You now must decide: is the mean distance between oil changes 3600 miles, or not? Explain your reasoning.
f) Which (if either) of the confidence intervals in (c) is appropriate? (Suggestion: look at your answer to (b).) Explain briefly.