Question

A bank will open a new branch in a particular neighborhood if it can be reasonably sure that at least 10% of the residents will consider banking at the new branch. The bank will use a significance level of 0.05 to make its decision. The bank does a survey of residents of a particular neighborhood and finds that 19 out of 100 random people surveyed said they’d consider banking at the new branch. Run a z-test for a single proportion and determine whether the bank should open the new branch, considering its standard policy.

i want a clear answer if the answer is on paper please,

Answer 1

Proportion (p0) = 0.10

Total number of sample (n) = 100

number of favourable events (X) = 19

We are interested in testing the hypothesis

Since P-value of a two tailed test is equal to

P = (1-0.9986501019683699)

P = 0.0013

Since, the test is two-tail test at \alpha = 0.05

Decision Rule: Reject the null hypothesis if the test statistic value is greater than the critical value 1.64

The statistic value, 3.0 is greater than the critical value 1.64. Hence, reject the null hypothesis.

Yes bank should open the new branch, considering its standard policy.