Question: In addition to measuring the engagement of each of the sampled employees, the consultants also measured the amount of supervisor support that each of the sampled employees perceive they receive. The amount of supervisor support is measured by a SUP score on a scale of one to fifty. Using the ENG and SUP scores, the consultants performed the following simple linear regression analysis:

In the questions that follow, let the population regression line be denoted by \(E\left( y|x \right)={{\beta }_{0}}+{{\beta }_{1}}x\), where the response variable y is ENG and the predictor variable x is SUP. Recall that the simple linear regression model assumes constant variance, i.e., \(\operatorname{var}\left( y|x \right)={{\sigma }^{2}}\) .

What is the value of the test statistic for testing H₀: E(y| x= 42) = 37, i.e., for testing the null hypothesis that the mean ENG score is 37 for employees having an SUP score of 42 ?