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Statistical Analysis of Expected Salaries, Demographics, and Other Factors: A Case Study from the Initial Student Survey

A statistical analysis case study focusing on expected salaries and demographic factors from an initial student survey.

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    Statistical Analysis of Expected Salaries, Demographics, and Other Factors: A Case Study from the Initial Student Survey Case Study Submission Cover Sheet Semester Project In supporting your answer s , where appropriate: • Use the data set that is pa rt of this assignment • Answer all questions in the order and space provided • Follow the steps that we discussed in class to conduct these analyses • Include a complete Hypothesis Statement • Include relevant tables from Excel (but not complete data set) • Cite specific values (p - value, critical value and alp ha) • Show/discuss the steps that you used to arrive at each answer • Follow the steps that we discussed in class to conduct procedure • Include ANOVA table • Conduct and show work for multiple comp arison tests (if required) Date Submitted: MM/DD/YYY Submitted by:

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    2 Question #1 1a: Using the sample data provided in the ISS Data Set, show and discuss the descriptive statistics that describes the projected salaries that were reported in the Initial Student Survey . o provide descriptive statistics for the projected salaries from the Initial Student Survey, we typically calculate: 1. Mean : The average projected salary. 2. Median : The middle value when the salaries are ordered. 3. Mode : The most frequently occurring salary value. 4. Standard Deviation : The amount of variation or dispersion from the mean. 5. Variance : The square of the standard deviation. 6. Range : The difference between the maximum and minimum salary. 7. Skewness : The asymmetry of the distribution of salaries. 8. Kurtosis : The sharpness of the peak of the salary distribution. 1b: Test the claim (alpha = .05) that expected salaries of all students upon graduation will be at least $ 6 5 ,000 . Assume population SD (Sigma) is known to be $ 20 000 • Null Hypothesis (H₀) : μ ≥ 65,000 (The average salary is at least $65,000) • Alternative Hypothesis (H₁) : μ < 65,000 (The average salary is less than $65,000) Given: • Population SD (σ) = 20,000 • Significance level (α) = 0.05

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    3 • Sample mean sal ary (xˉ \ bar{x}xˉ) and sample size (n) are assumed to be provided in the dataset. The test statistic is calculated using the Z - test formula: Where: • μ0=65,000 \ mu_0 = 65,000μ0 =65,000 (the hypothesized population mean) • xˉ \ bar{x}xˉ is the sample mean • n nn is the sample size • σ \ sigmaσ is the population standard deviation You would compare the calculated Z to the critical Z - value (Z_critical) at a significance level of 0.05. If Z is less than the critical value, we reject the null hypothesis. 1c: Test the claim (alpha = .05 and at alpha = . 10 ) that expected salaries upon graduation will be $ 65,5 00 . Assume population SD (Sigma) is known to be $ 20 000 . • Null Hypothesis (H₀) : μ = 65,500 (The average salary is $65,500) • Alternative Hypothesis (H₁) : μ ≠ 65,500 (The average salary is not $65,500) Given: • Population SD (σ) = 20,000 • Significance level (α) = 0.05 and 0.10 • Sample mean salary (xˉ \ bar{x}xˉ) and sample size (n) are assumed to be provided. For a two - tailed test, the Z - test statistic is:

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    4 Whe re: • μ0=65,500 \ mu_0 = 65,500μ0 =65,500 You would compare the calculated Z to the critical Z - values for α = 0.05 (Z_critical = ±1.96) and α = 0.10 (Z_critical = ±1.645). If the absolute value of Z is greater than the critical value, we reject the null hypothesis. Discuss the difference or similarities of these findings. 1. Comparison of Results (1b and 1c) : o For α = 0.05 : A more stringent threshold means you're less likely to reject the null hypothesis. If the test result (Z) falls near the critical val ue, it may indicate insufficient evidence to reject the hypothesis of the expected salary being $65,500. o For α = 0.10 : A less stringent threshold increases the likelihood of rejecting the null hypothesis, so we might see more rejections of H₀ here compared to α = 0.05. If the calculated Z - values in both tests do not fall in the rejection region, we fail to reject the null hypothesis and conclude that the expected salary is not significantly different from the hypothesized values ($65,000 and $65,500).

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