Business Analytics III - Module 3 PDF

Prepared by Kamalika Dasgupta BUSINESS ANALYTICS – III MODULE 3 Course Description  Data Analysis Tool  Z-test for two Sample testing for means  t-test for two Sample  Testing two variances  F-test and F-distribution Z-test for two sample testing for means  Testing the difference betwee...

Prepared by Kamalika Dasgupta BUSINESS ANALYTICS – III MODULE 3 Course Description  Data Analysis Tool  Z-test for two Sample testing for means  t-test for two Sample  Testing two variances  F-test and F-distribution Z-test for two sample testing for means  Testing the difference between the means of two ‘independent’ population (μ1 and μ 2)  Where population standard deviations (σ1 and σ2) are known  Null hypothesis is H0: μ1 - μ2 = 0  Alternative hypothesis is H1: μ1 - μ2 ≠ 0 Test Statistic Rejection-Acceptance Criteria Application in MS-Excel  Concept Video Z-test for two sample means in MS Ex cel Application in MS-Excel Let’s suppose that a student wants to figure out if biology professor or English professors know more memes. The student writes a meme quiz and springs it on 14 unsuspecting biology professors and 18 unsuspecting English professors during office hours. The biology professors get the following scores: 3,7,11,0,7,0,4,5,6,2,4,7,2,93,7,11,0,7,0,4,5,6,2,4,7,2,9 and the English professors score: 5,5,4,5,4,5,7,2,6,2,2,7,2,6,4,2,5,25,5,4,5,4,5,7,2,6,2,2,7,2,6,4,2 ,5,2 We’ll assume that the population variance of the biology professor scores is σ1^2=3 and the population variance of the English professor scores is σ2^2=2. Step by Step  Go to excel -> Insert the data in two columns  Go to Data -> Data Analysis -> Select the Last z-test option  Variable 1 range put the 1st variable value -> Variable 2 range put the 2nd variable value  Hypothesized mean difference put 0-> Put the respective variance values in variable 1 variance and variable 2 population variance-> Put the value of ⍺ (Whatever is given in the question) -> Select new worksheet for the result  Reject the null hypothesis if the absolute value of Z is greater than the tabulated value (the last value in the output range)  Alternatively reject null hypothesis if “P-value” is less than the value of ⍺ t-test for two sample  Testing the difference between the means of two ‘independent’ population (μ1 and μ 2)  Where population standard deviations (σ1 and σ2) are unknown  Null hypothesis is H0: μ1 - μ2 = 0  Alternative hypothesis is H1: μ1 - μ2 ≠ 0 Test Statistic With degrees of freedom = (n1+n2- 2) = difference between two sample means = difference between two population & means & = two sample variances Rejection-Acceptance Criteria Application in MS-Excel  Concept Video t-test for two sample means in MS-Exc el Application in MS-Excel Hypotheses  We apply two sample t-test  We test the null hypothesis H0 : μ1 – μ2 = 0  Against the alternative hypothesis H1: μ1 – μ2 > 0  At level of significance (⍺) = 0.01 Step by Step  Go to excel -> Insert the data for two samples in two columns  Go to Data -> Data Analysis -> Select the “two-sample t- test with unequal variance” option  Variable 1 range put sample 1 values-> Variable 2 range put sample 2 values  Hypothesized mean difference put 0-> Put the value of ⍺ (Whatever is given in the question-> Select new worksheet for the result  Reject the null hypothesis if the t value is greater than the critical one-tail or two tail value Testing two variances – F Test  Testing for equality of two “independent” population variances (σ1^2 and σ2^2)  Where the two population means (μ1 and μ2) are “unknown”  Null hypothesis is H0: σ1^2 - σ2^2 = 0  Alternative hypothesis is H1: σ1^2 - Test Statistic Rejection-Acceptance Criteria Application in MS-Excel  Concept Video F-test for two independent populat ion variances Application in MS-Excel Hypotheses  We apply two sample F-test  We test the null hypothesis H0 : σ1^2 - σ2^2 = 0  Against the alternative hypothesis H1: σ1^2 - σ2^2 ≠ 0  At level of significance (⍺) = 0.05 Step by Step  Go to excel -> Insert the data for two samples in two columns  Go to Data -> Data Analysis -> Select the “two-sample F-test with unequal variance” option  Variable 1 range put sample 1 values-> Variable 2 range put sample 2 values  Put the value of ⍺ (Whatever is given in the question-> Select new worksheet for the result  Reject the null hypothesis if the t value is greater than the critical one-tail or two tail value  Alternatively reject null hypothesis if “P-value” is less than the value of ⍺ THANK YOU FOR YOUR ATTENTION !