1. A manager wishes to find out whether there is a relationship between the age of his employees and the number of sick days they take each year. The data is given below:

Question

Age (X) 18 26 39 48 53 58 24 50
Days (Y) 16 12 9 5 6 2 10 7

a. What is the null hypothesis?
b. What is the strength and the direction of relationship?

c. Is the relationship significant?
d. What proportion of the number of sick days can be explained by the age of the employee?
e. In a sentence or so, give an appropriate interpretation of the analysis results.

Answer 1

Use the Pearson r.

To find if there is a statistically significant linear relationship between hours worked and error rate, use N-2 for degrees of freedom at the appropriate significance level for the test you are doing. Use a table for critical or cutoff values for a Pearson r. Compare the value from the table to the value you calculated using a formula for the Pearson r. If the value you calculate exceeds the critical value from the table, the null will be rejected. There will be a linear relationship in the population and the test will be statistically significant. If the value you calculate does not exceed the critical value from the table, then the null will not be rejected and you cannot conclude a linear relationship in the population.

I hope this brief explanation will get you started.

Answer 2

Correction - the first sentence should read as follows:

To find if there is a statistically significant linear relationship between age and number of sick days, use N-2 for degrees of freedom at the appropriate significance level for the test you are doing.

Sorry for any confusion.