Question

A salesman who is on the road visiting clients thinks that, on average, he drives the same distance each day of the week. He keeps track of his mileage for several weeks and discovers that he averages 122 miles on Mon- days, 203 miles on Tuesdays, 176 miles on Wednesdays, 181 miles on Thursdays, and 108 miles on Fridays. He wonders if this evidence contradicts his belief in a uni- form distribution of miles across the days of the week. Explain why it is not appropriate to test his hypothesis using the chi-square goodness-of-fit test.

Answer 1

The conditions are not met.

Explanation:

The conditions for the chi square test for goodness of fit are

1) the sample is a random sample

2) the variable under study is categorical

3) all expected value of the number of sample observations are greater or equal to 5.

A)The observations must be independent

B) for 2 categories the expected values must be at least 5

C) for the 3 categories the expected values must be at least 1 and no more than 20% may be smaller than 5

The observations given may not be independent i.e have equal chances of occurrences or are maybe dependent on each other in the sense that there maybe a limit for his traveling mileage or the a limit for petrol ( fuel ) usage . So if he is required to drive 500 miles in a week each day mileage depends on the other day mileage .

Also we are given the information that keeps track of his mileage for several weeks, but we are not sure if several refers to more than 5 .

As both conditions are not clearly satisfied it is not appropriate to test his hypothesis using the chi-square goodness-of-fit test.

The sample must also be a random sample.

Here he has taken the mean of all the days.