Problem 1: You Work For A Major Sporting Goods Retail

Problem 1problem 1you Work For A Major Sporting Goods Retailer And Ar

Problem 1: You work for a major sporting goods retailer, and are responsible for evaluation of personnel. There are employees of different years of service: “Less than 1 Year,” “1 to 2 Years,” “3 to 5 Years,” and “Over 5 Years.” Management wants to investigate the “Invoicing Department” employees’ subjective evaluations by department managers. Managers have rated employees by performance groups of “Below Average,” “Average,” and “Above Average.” A sample of 80 employee evaluations has been collected. We want to be 90% confident about the independence of "Managers' Employee Ratings" with the different “Employee Years of Service.”

Calculate the appropriate statistical tests in Excel to determine whether there is a statistically significant association between employee years of service and performance ratings. Show all work, including chi-square calculations, degrees of freedom, and critical value comparisons. Attach the Excel spreadsheet with your calculations.

Paper For Above instruction

In the context of personnel evaluation within the retail sporting goods sector, assessing the independence between employee years of service and their performance ratings is crucial for unbiased human resource practices. This investigation employs the chi-square test of independence to determine whether employee tenure correlates with performance evaluations, which can influence management decisions and retention strategies.

The null hypothesis (H₀) posits that there is no association between years of service and performance ratings; in other words, the ratings are independent of employee tenure. The alternative hypothesis (H₁) suggests that there is an association, indicating dependence between these variables. To test these hypotheses, we construct a contingency table based on the sample data, calculate the expected frequencies under the assumption of independence, and then compute the chi-square test statistic.

The data involves categorical variables: four levels of employee tenure and three performance ratings. The chi-square test statistic is calculated as the sum of the squared differences between observed and expected frequencies divided by expected frequencies across all cells:

χ² = Σ [(O - E)² / E]

Using Excel, the observed frequencies are entered in a table, and expected frequencies are calculated based on row and column totals. The degrees of freedom (df) for the test are determined by:

df = (number of rows - 1) × (number of columns - 1)

For this problem, df = (4 - 1) × (3 - 1) = 3 × 2 = 6. The critical value for df = 6 at the 0.10 significance level (since the confidence is 90%) can be obtained from the chi-square table, which is approximately 10.645.

If the calculated χ² exceeds the critical value, we reject H₀, indicating that employee years of service and performance ratings are not independent. If it does not, we fail to reject H₀, suggesting the ratings are independent of tenure.

This statistical approach provides a robust method for management to assess whether subjective performance evaluations are influenced by employee tenure, which has implications for bias detection and fair evaluation practices within the organization.

Problem 2 Discussion

In evaluating the durability of fabrics for potential store branding, a two-factor experimental design was used, examining three fabric weaves (Denim, Twill, Canvas) and five fiber blends. Each combination was tested using abrasion tests, measuring the number of rubs until wear begins. The analysis involves assessing whether the fabric type affects durability (the primary interest) while controlling for variation introduced by different fiber blends. Blocked on fiber blends, analysis of variance (ANOVA) tests the hypothesis that all three fabrics are equally durable.

The hypotheses for this ANOVA are:

• Ho: μ_Denim = μ_Twill = μ_Canvas
• Ha: At least one mean durability differs

Calculations involve determining sum of squares for treatment (SST), error (SSE), total (SSTotal), and corresponding degrees of freedom. The F-test statistic compares mean square treatment (MST) to mean square error (MSE). The critical F-value is obtained from F-distribution tables, considering the degrees of freedom for treatments and error.

If the test statistic exceeds the critical value, the null hypothesis is rejected, indicating significant differences among fabric durabilities. Otherwise, the fabrics are considered equally durable under the tested conditions.

This assessment informs production decisions and marketing strategies for developing a durable, competitive store brand of hunting clothes.

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