Sales Analysis and T-Test Results for Multiple Locations
School
Humber College**We aren't endorsed by this school
Course
FIN 3020
Subject
Statistics
Date
Dec 11, 2024
Pages
12
Uploaded by MagistratePorcupine1970
Table: Sales (million $) in 2024Q1. AObservationLocation1 Location2Location31328723258656439889874675490598768361001891237120661458321231694343451076676111508749121151321091363715914230145260151652542301625721016517879818718766780191401191122012012090Q1. BT-test for each pair of locations Test for Equality of Population Means(for each pair
For Location 1 & Location 2t-Test: Two-Sample Assuming Unequal VariancesLocation1Location2Mean101.35108.1Variance3626.8711 3082.5158Observations20200df38t Stat-0.368534P(T<=t) one-tail0.3572603t Critical one-tail1.6859545P(T<=t) two-tail0.7145205t Critical two-tail2.0243942For Location 2 & Location 3t-Test: Two-Sample Assuming Unequal VariancesLocation2Location3Mean108.1103.9Variance3082.5158 4259.7789Observations2020Hypothesized Mean Di0df37t Stat0.219204P(T<=t) one-tail0.413848t Critical one-tail1.6870936P(T<=t) two-tail0.8276959t Critical two-tail2.0261925For Location 1 & Location 3t-Test: Two-Sample Assuming Unequal VariancesLocation1Location3Mean101.35103.9Variance3626.8711 4259.7789Hypothesized Mean DifferenceSince P(0.71)>0.05, Fail to Reject H0, means are not significantly differentSince P(0.82)>0.05, Fail to Reject H0, means are not significantly differentTest for Equality of Population Means(for each pair of locations).Use a two-sample t-test to compare means for each pair of locations, assuming unequal variances if variances are found to be unequal.Hypotheses for each pair: Location 1 & Location 2Null hypothesis H0: μ1=μ2Alternative hypothesis Ha: μ1≠μ2Significance level: 0.05Hypotheses for each pair: LocaLocation 3Null hypothesis H0: μ1=μ2Alternative hypothesis Ha: μ1≠Significance level: 0.05Hypotheses for each pair: LocaLocation 3
Observations2020Hypothesized Mean Di0df38t Stat-0.128413P(T<=t) one-tail0.4492497t Critical one-tail1.6859545P(T<=t) two-tail0.8984994t Critical two-tail2.0243942Q1. CChi-sqStdev for Location 1:60.22350917.36Stdev for Location 2:55.52040914.76Stdev for Location 3:65.26698220.39Chi-sq critical value10.12Since P(0.89)>0.05, Fail to Reject H0, means are not significantly differentSince chi-sq value is gSince chi-sq value is gSince chi-sq value is gLocation 3Null hypothesis H0: μ1=μ2Alternative hypothesis Ha: μ1≠Significance level: 0.05Test if Standard Deviation of Sales in Each Location is Less Than 63.Use a one-sample chi-square testfor standard deviation comparison.Hypotheses for each location:Null hypothesis H0: σ≥63Alternative hypothesis Ha: σ<63Significance level: 0.05
F-test for each pair of locations For Location 1 & Location 2F-Test Two-Sample for VariancesLocation1 Location2Mean101.35108.1Variance3626.8713082.516Observations2020df1919F1.176594P(F<=f) one-tail0.363316F Critical one-tail2.168252For Location 1 & Location 3F-Test Two-Sample for VariancesLocation1 Location3Mean101.35103.9Variance3626.8714259.779Observations2020df1919F0.851422P(F<=f) one-tail0.364749F Critical one-tail0.461201For Location 2 & Location 3F-Test Two-Sample for VariancesLocation2 Location3Mean108.1103.9Variance3082.5164259.779Observations2020df1919F0.723633P(F<=f) one-tail0.24375F Critical one-tail0.461201Since P(0.36)>0.05, Fail to Reject H0, variances are not significantly dSince P(0.36)>0.05, Fail to Reject H0, variances are not significantly dSince P(0.24)>0.05, Fail to Reject H0, variances are not significantly dTest for Equality of Ppair of locations).Use an F-test to comparlocations.Hypotheses for eacNull hypothesis H0Alternative hypothSignificance level: Hypotheses for eachNull hypothesis H0:Alternative hypotheSignificance level: 0Hypotheses for eachNull hypothesis H0: Alternative hypothesSignificance level: 0
ation 2 & ≠μ2ation 1 &
greater than chi sq critical value (17.36>10.11), we fail to rejectthe null hypothesis. Standard deviation is not significantly less than 63.greater than chi sq critical value (14.76>10.11), we fail to rejectthe null hypothesis. Standard deviation is not significantly less than 63.greater than chi sq critical value (20.39>10.11), we fail to rejectthe null hypothesis. Standard deviation is not significantly less than 63.≠μ2
differentdifferentdifferentPopulation Variances(for each re variances for each pair of ch pair: Location1 and Location30: σ1^2=σ2^2 hesis Ha: σ1^2≠σ2^2 0.05h pair: Location2 and Location3: σ1^2=σ2^2 esis Ha: σ1^2≠σ2^2 0.05h pair: Location1 and Location2σ1^2=σ2^2 sis Ha: σ1^2≠σ2^2 0.05
Sales (million $234120314.74-80.74-202.86876450688.03187.97170.43450120314.74135.26-202.869007801061.33-161.33543.73786580835.09-49.09317.4912090280.80-160.80-236.80345300518.35-173.350.75450350574.91-124.9157.31568230439.17128.83-78.43890450688.03201.97170.43460210416.5543.45-101.05340120314.7425.26-202.86254100292.12-38.12-225.48289140337.36-48.36-180.24802450688.03113.97170.43AVERAGE SALES517.6SUMMARY OUTPUTRegression StatisticsMultiple R0.8740074980957R Square0.76388910672751Adjusted R Squar0.74572673032193Standard Error134.961222155339Observations15ANOVAdfSSMSFRegression1 766082.690686 766082.6907 42.0588743273134Residual13 236788.909314 18214.53149Total141002871.6CoefficientsStandard Errort StatP-valueAdvertising expense (million $)Predicted Sales Residuals (Actual - Predicted)Difference between Predicted sales - mean of sales1. Regression Equation:The Interceptand X Variable 1coefficients will be displayed in the output. Theequation will be:Sales=Intercept+(Coefficient of X Variable 1) * Advertising expense
Intercept178.997082535299 62.7717204368 2.851556103 0.01361628257321Advertising expen1.131190147432190.17442422071 6.485281361 2.0501352741E-05
41152.2229047.29SSE236788.9141152.22SSR766082.69295637.31SST1002871.60100798.23SEE134.9656072.250.573284.856151.1429047.2910211.7141152.2250842.9932485.1229047.29SUM of squares766082.69Significance F2.05013527E-05Lower 95%Upper 95%Lower 95.0% Upper 95.0%Square of the differencee regression 010020030040001002003004005006007008009001000f(x) = 1.13119014743219 x + 178.9970Linear regression of sales oAdvertising expeSales ($millions)
43.3870251914314.607143.38703 314.6071398790.754369528081.5080110.75437 1.50801076678
50060070080090082535299on advertising expense ense ($millions)