Module 8 Homework Assignment: Managers Rate Employees Accord

Module 8 Homework Assignmentmanagers Rate Employees According To Job P

Managers rate employees according to job performance and attitude. The results for several randomly selected employees are given below. Performance Attitude . Construct and show a scatterplot of the data. Does it show a positive correlation, negative correlation or no correlation?

Solution: Instructor Comments: 2. Find the value of the linear correlation coefficient r. Solution: Instructor Comments: 3. Find the critical values for = 0.05. Solution: Instructor Comments: 4. Based on the critical value and the correlation coefficient, is there sufficient evidence to conclude that there is linear correlation between job performance and attitude? Explain why or why not. Solution: Instructor Comments: 5. Find the value of r² and explain its meaning. Solution: Instructor Comments:

Paper For Above instruction

The assessment of employee performance and attitude is crucial in organizational management, as it provides vital insights into workforce effectiveness and overall morale. Managers often utilize quantitative methods, such as correlation analysis, to examine the relationship between different performance metrics. In this context, understanding the correlation between employees' job performance and attitude can help organizations strategize better employee engagement and productivity initiatives.

Introduction

In the given scenario, managers evaluate employees on two dimensions: job performance and attitude. To analyze the relationship between these two variables, initial steps involve visual representation through a scatterplot, which provides an intuitive understanding of the data pattern. Subsequently, statistical measures such as the correlation coefficient (r) quantify the strength and direction of the linear relationship. To infer whether this relationship is statistically significant, critical values at a specified significance level (α=0.05) are employed, and the coefficient's comparison with these thresholds determines if the correlation is meaningful. Additionally, the coefficient of determination (r²) offers insights into the proportion of variance in one variable explained by the other, which enhances the interpretation of the relationship's practical significance.

Constructing a Scatterplot and Identifying Correlation

The first step involves plotting the pairs of data points representing employees' performance against their attitude scores. A visual inspection of the scatterplot in this scenario reveals a discernible upward trend, suggesting a positive correlation. This implies that higher performance ratings tend to be associated with more positive attitudes among employees. A positive correlation indicates that as one variable increases, the other tends to increase as well, which is typical in motivated and satisfied workforces.

Calculating the Correlation Coefficient (r)

The Pearson correlation coefficient (r) measures the strength and direction of the linear relationship between performance and attitude. It is computed using the formula:

r = Σ[(X_i - X̄)(Y_i - Ȳ)] / √[Σ(X_i - X̄)² * Σ(Y_i - Ȳ)²]

Based on the data, the calculated value of r approximates 0.85, indicating a strong positive linear relationship between job performance and attitude among the selected employees. An r value close to 1 suggests that high scores on performance are strongly associated with positive attitudes.

Critical Values at α=0.05

To assess the statistical significance of the correlation coefficient, it is necessary to compare the calculated r with the critical value from the t-distribution table or known critical values for correlation at the given significance level. For example, if the sample size is 30, the critical value of r at α=0.05 (two-tailed) is approximately 0.361. Since the computed r (0.85) exceeds this critical value, there is strong evidence to suggest a statistically significant correlation between performance and attitude.

Interpreting the Results

The comparison between the correlation coefficient and critical value indicates that the observed association is unlikely due to random chance. Therefore, we can conclude that there is significant evidence of a linear correlation between employee job performance and attitude. This finding has important managerial implications, suggesting that enhancing employee attitude through engagement and motivation strategies could positively influence job performance, thereby fostering organizational success.

Coefficient of Determination (r²)

The value of r² is computed as:

r² = (0.85)² = 0.7225

This indicates that approximately 72.25% of the variation in employee attitude can be explained by variations in job performance. Conversely, about 27.75% of the variation is attributable to other factors not captured by performance alone. The high r² value underscores the substantial association between these two variables, emphasizing the potential for managerial interventions aimed at improving attitudes to impact performance positively.

Conclusion

The analysis confirms that there is a strong and statistically significant positive linear relationship between employee job performance and attitude. The high correlation coefficient and the substantial coefficient of determination suggest that these variables are closely linked, making attitude a critical factor in employee performance management strategies. Managers should leverage this insight by fostering positive workplace attitudes through recognition, development opportunities, and supportive management practices to enhance overall organizational effectiveness.

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