Analyzing the Relationship Between Tenure and Workplace Performance- A Case Study Using CV Data

To determine whether there is a significant linear correlation between age and salary at XYZ Company, we have the calculated value of the linear correlation coefficient (r) as 0.518. For a significance level of α = 0.05, the critical value of r can be found in the provided CV of the r spreadsheet. We look for the critical value that corresponds to r = 0.518, which also has a sample size (n) of 28. The critical value of r for α = 0.05 and n = 28 is approximately 0.361. Next, we need to find the p-value corresponding to the calculated value of r. The p-value represents the probability of observing a correlation coefficient as extreme as the calculated value under the assumption of no correlation (null hypothesis).

To test the hypothesis that there is no linear correlation between age and salary, we set up the null and alternative hypotheses as follows:

Null Hypothesis (H0): No linear correlation exists between age and salary (r = 0).

Alternative Hypothesis (Ha): A linear correlation exists between age and salary (r ≠ 0).

Since the sample size is relatively small (n = 28), we will use a t-distribution to find the p-value. The formula for the t-statistic in this case is:

t = r * sqrt((n – 2) / (1 – r^2))

t = 0.518 * sqrt((28 – 2) / (1 – 0.518^2))

t ≈ 5.286

Using the t-table for a two-tailed test, we find that the p-value corresponding to t ≈ 5.286 is significantly less than 0.001 (p < 0.001). Since the p-value is less than the significance level, α = 0.05, we reject the null hypothesis. Therefore, we can conclude that there is sufficient evidence to support the claim of a linear correlation between age and salary at XYZ Company. The positive value of r = 0.518 suggests a moderate positive linear relationship between age and salary. Therefore, as the employees’ age increases, their salary tends to increase as well.