Question

A university would like to examine the linear relationship between a faculty​ member's performance rating​ (measured on a scale of​ 1-20) and his or her annual salary increase. The table to the right shows these data for eight randomly selected faculty members. Complete parts a and b

Rating   Increase
17   2300
18   2600
12   1900
14   1700
15   1900
15   2700
17   1900
15   1900

find t statistic=

find p-value=

conclusion

Answer 1

Let denotes the linear relationship between a faculty​ member's performance rating​ (measured on a scale of​ 1-20) and his or her annual salary increase.

To test against

Here

sample correlation coefficient

and sample size n = 8

The test statistic can be written as

which under H₀ follows a t distribution with n-2 df.

We reject H₀ at 0.05 level of significance if P-value < 0.05

Now,

The value of the test statistic

and P-value =

Since P-value > 0.05, so we fail to reject H₀ at 0.05 level of significance and we can conclude that there is no significant linear relationship between a faculty​ member's performance rating​ (measured on a scale of​ 1-20) and his or her annual salary increase.