A lending institution Wanted to investigate it there was an...

A lending institution Wanted to investigate it there was an association between the loan officer (A B, C) reviewing a loan application and the loan approval decision (approved, paused, rejected), A sample of 301 loan applications are evaluated Approved. Paused. Rejected. Total. Officer A. 33. 31. 40. 104. Officer B 45. 25. 21. 91. Officer C 25. 17. 64. 106. Total 103. 73. 125. 301. The test statistic and conclusion of the hypothesis test at the 2.5% significant level is A. 29.665, reject the null hypothesis B. 29.665, do not reject the null hypothesis C. None of the presented options, Da D. 30,426, reject the null hypothesis E. 30,426, do not reject the null nypothesis

Transcript

00:01 Hello students, let us do this question.

00:03 Hypothesis to be tested here is h0.

00:06 There is no association between loan officer abc reviewing a loan application and the loan approval decision that is approved, paused and rejected.

00:21 And the alternative hypothesis is there is association between the two categorical variables.

00:30 We know that we use chi -square test for testing the association between the two categorical variables.

00:36 The test statistic is chi -square is equal to summation over i oi minus ei bracket square upon ei where oi is the observed frequency, ei is the expected frequency for the ith sale.

00:53 It is computed as row total for that sale into column total for that sale upon grand total.

01:01 So let us say for the first sale where officer is a and status is approved, we have oi as 33.

01:10 We have row total for that sale as 104 and column total for that sale as 103.

01:19 So ei will be 104 to 103 divided by grand total is total number of observations which is 301.

01:30 So we get ei for the officer a and approved status as 35 .59.

01:38 In the same way expected frequency for each sale are computed.

01:43 Now the quantity chi -square is computed for the each sale using this formula where oi is the observed frequency and ei is the expected frequency.

01:54 Table given here contains observed frequencies which is nothing but the first value into the sale.

02:00 Then in round brackets the expected frequencies are given and in the square bracket the chi -square quantity computed for each sale is given...

Question

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