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

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Statistical Analysis of Expected Salaries, Demographics, and OtherFactors: A Case Study from the Initial Student SurveyCase Study Submission Cover SheetSemester ProjectIn supporting your answers, where appropriate:•Use the data set that is part of this assignment•Answer all questions in the order and space provided•Follow the steps that we discussed in class to conductthese analyses•Include a complete Hypothesis Statement•Include relevant tables from Excel (but not complete data set)•Cite specific values (p-value, critical value and alpha)•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 comparison tests (if required)Date Submitted: MM/DD/YYYSubmitted by:

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2Question #11a:Using thesampledata provided in theISSData Set, show and discuss the descriptivestatistics that describes the projected salaries that were reported in the Initial StudentSurvey.o provide descriptive statistics for the projected salaries from the Initial Student Survey, wetypically 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 salariesof all studentsupon graduation will be atleast $65,000.Assume population SD(Sigma)is known tobe $20000•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 salary (xˉ\bar{x}xˉ) and sample size (n) are assumed to be provided inthe 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•nnn is the sample size•σ\sigmaσ is the population standard deviationYou would compare the calculated Z to the critical Z-value (Z_critical) at a significancelevel of 0.05. If Z is less than the critical value, we reject the null hypothesis.1c:Testthe claim (alpha = .05 and at alpha = .10) that expected salaries upon graduation willbe $65,500.Assume population SD(Sigma)is known to be$20000.•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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4Where:•μ0=65,500\mu_0 = 65,500μ0=65,500You 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 thecritical value, we reject the null hypothesis.Discuss the difference or similarities of these findings.1.Comparison of Results (1b and 1c):oFor α = 0.05: A more stringent threshold means you're less likely to rejectthe null hypothesis. If the test result (Z) falls near the critical value, it mayindicate insufficient evidence to reject the hypothesis of the expected salarybeing $65,500.oFor α = 0.10: A less stringent threshold increases the likelihood of rejectingthe null hypothesis, so we might see more rejections of H₀ here compared toα = 0.05.If the calculated Z-values in both tests do not fall in the rejection region, we fail to reject thenull hypothesis and conclude that the expected salary is not significantly different from thehypothesized values ($65,000 and $65,500).

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