LeRoy Dewey, chief of operations of the Johnston City Telephone Service, is conc

Question

LeRoy Dewey, chief of operations of the Johnston City Telephone Service, is concerned about accident rates among his work crews, and wishes to take steps to address the problem. As a first step he has decided to see where the problem lies. For each of the 30 work crews under his direction he collects data on accident rates (over the past six months) and various demographic features of the crew. He is struck in particular by the relationship that he sees in the data concerning the accident rates and the years of experience of the crew supervisors. The data are given in the table below. To see what has stuck Dewey, we regress accident rates against the years of experience using Stata. The Stata output is given below.

A. What is the slope of the relationship? How significant is it? (Is it significantly different from zero?)

B. To deal with accidents, Dewey wishes to provide education on accident prevention to his crew supervisors. He had thought to target supervisors with higher number of years of experience, in the belief that they needed the education more (having been further from their initial training on accident prevention). Based on the results of this analysis, he is now considering targeting the supervisors with less years of experience. Do you find this conclusion a good conclusion to draw from these data? If not, why not?

Crew NumberAccident Rate |Supervisor Experience 3.6 10.6 10.7 5.2 7.8 5.4 7.3 11.9 14.9 10.6 0.5 1.4 13.6 0.8 14.0 7.2 7.2 14.4 0.7 14.2 3.2 5.3 10.8 6.1 3.3 13.0 6.7 13.7 5.4 13.1 2.5 2.0 1.8 1.0 0.8 2.1 1.7 3 4 2.0 0.5 3.4 1.7 1.8 1.6 1.4 1.3 2.9 0.0 2.2 2.3 2.1 1.2 2.0 1.2 1.2 0.7 0.1 0.5 2.0 0.8 10 12 13 14 15 16 17 18 19 20 21 23 24. 25 26 27 28 29 30

Explanation / Answer

Answer:

Part a

The slope of the relationship is given as 2.045927. For checking the significance of this slope by using t test, p-value is given as 0.00 which is less than alpha value 0.05. So, we reject the null hypothesis that there is no any statistically significant relationship exists between the two variables accident rate and supervisor experience. The slope is statistically significant and it is significantly different from zero.

Part b

For the overall linear regression model, the F test statistic is given as 4.27 with the p-value as 0.0480. This p-value is less than level of significance or alpha value 0.05. So, at 5% level of significance, we reject the null hypothesis that there is no statistically significant relationship exists between two variables such as accident rate and supervisor experience. There is sufficient evidence that there is a statistically significant linear relationship exists between given two variables. So, conclusion given in the scenario is a good conclusion to draw from given data.

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