Question

The Bank of America wants to assess the recommendations before the change vs. the recommendations after the change as a result of a recent internal policy change. It has gathered the follow data:

1. 152 Bank of America customers were studied.

2. Of the 152, 102/152 recommended the bank before the change whist 50/152 did not recommend the bank before the change.

3. Of the 152, 132/152 recommended the bank after the change whilst 20/152 did not recommend the bank after the change.

1. Use the information above to answer questions (a) and (b).
   1. Perform a statistical test to see whether the proportion of members who would recommend the bank of america have increased because of the change.
   2. Construct a 99% confidence interval for the difference of the proportions, before and after the change, of members who would recommend the bank of america

Answer 1

Let , be the Bank of America wants to assess the recommendations before the change and be the Bank of America wants to assess the recommendations after the change.

Given : n1=152 , x1=102 , n2=152 , x2=132

The sample proportions are given by ,

The pooled estimate is ,

a) Hypothesis : Vs  

The test statistic is ,

The Critical value is ,

; From standard normal probability table

Decision : Here , the value of the test statistic lies in the rejection region.

Therefore , reject Ho.

Conclusion : Hence , there is sufficient evidence to support the claim that the proportion of members who would recommend the bank of america have increased because of the change.

b) The 99% confidence interval for the difference of the proportions, before and after the change, of members who would recommend the bank of america is ,

; , From standard normal probability table