Question

A financial services company has 38 female top executives (presidents or vice presidents) among its 416 senior managers in its Banking Services division, while only 17 female top executives among its 309 senior managers in its Investment Services division. Test at the 0.01 significance level if this reveals the Banking Services division has significantly more female top executives in higher levels of management.

a. State the decision rule. (Round the final answer to 3 decimal places.)

If z  is more than _____ reject H₀.

=

b. Compute the pooled proportion. (Round the final answer to 5 decimal places.)

p_c =

c. Compute the value of the test statistic. (Round the final answer to 3 decimal places.)

The test statistic is=

Answer 1

Total number of sample 1 (n1) = 416
Total number of sample 2 (n2) = 309
number of favourable events (X1) = 38
number of favourable events (X2) = 17

We are interested in testing the hypothesis

Decision Rule: Reject the null hypothesis if the test statistic value is less than the critical value -2.3263 or greater than the critical value 2.3263
The statistic value, 1.8266 is greater than the critical values -2.3263 . Therefore, we fail to reject the null hypothesis.