Population 2 = Bay Health o Hypotheses ▪ H0: σ1 = σ2 ▪ H1: σ1 ≠ σ2 (population variances are different) ● Step 3: set a value for the significance level, ∞ o Set ∞ = 0.05 ● Step 4: Calculate the F-test statistic o Finding F ▪ F = s1 / s2 ▪ = 0.8464 / 0.5041 = 1.679 ● Step 5: Determine the critical value (F-score) o Degrees of Freedom
▪ D1 = (n1 – 1) = (20 – 1) = 19 ▪ D2 = (n2 – 1) = (20 – 1) = 19 o F-Score ▪ Two-tail test → ∞/2 = 0.025 ▪ Area in right tail of distribution (0.025 column) ▪ D1 = 19 and D2 = 19 ▪ → 2.526 ● Step 6: Compare the test statistic (F) with the critical value (F-score) o 1.679 (F) < 2.526 (F-score) → do not reject H0 ● Step 7: State your conclusions o Fail to reject null hypothesis ▪ Do not have evidence that population variances are diff for the two hospitals ▪ CANT SAY variances are equal, but business says we probably have no reason to investigate the diff in stay time for each of the hospitals ● Using PHStat2 to Compare Two Population Variances o Procedures ▪ Add-ins > Two-Sample Tests (Summarized Data) > F Test for Differences in Two Variances ▪ Fill in values where needed - Sample SD - Level of significance, ∞ - Population 1 sample size and sample variance - Population 2 sample size and sample variance - Two-tail test or upper-tail test o Results ▪ Intermediate Calculations - F Test Statistic - Population 1 Sample DF - Population 2 Sample DF
▪ Two-Tail Test - Upper Critical Value (F-Score) - P-value - Whether or not to reject the null hypothesis
Chapter 14: Correlation and Simple Regression Analyses ● Intro o Correlation & Investments ▪ Investors strive to achieve uncorrelated investments to reduce the risk of one of their stocks affecting the other OR all increasing / decreasing at one time o Techniques that find relationships b/w 2 factors ▪ Correlation Analysis - Determines strength and direction of the relationship b/w two variables - Hypothesis test – det. if strength b/w 2 variables is strong enough to be useful ▪ Simple regression - Describes the relationship b/w 2 variables using a linear equation - Predict variable 1 given specific value of variable 2, and vice versa - Hypothesis to det. if results are accurate enough to be useful o Applications in Business ▪ Realtors want to est. relationship b/w living space and eventual selling price in particular town ▪ Best Buy manager wants to know effect of dropping printer price $10 will have on demand in next week ▪ Coke wants to predict extent to which running a 30-second Super Bowl ad will improve sales ➢ 14.1 – DEPENDENT AND INDEPENDENT VARIABLES o Terms ▪ Independent Variable (X) – explains the variation (change) in another variable ▪ Dependent variable (Y)
▪ X → Y ▪ Does NOT work in reverse ➢ 14.2 – CORRELATION ANALYSIS o The Basics ▪ Measure strength / direction of linear relationship b/w 2 variables ▪ Calculate correlation coefficient (R) - Provides value describing relationship ▪ Hypothesis test to decide if relationship b/w 2 variables is strong enough to be considered statistically significant
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- Normal Distribution, Null hypothesis, Hypothesis testing, Statistical hypothesis testing