Question

One study reports that 27 ​% of newly hired MBAs are confronted with unethical business practices during their first year of employment. One business school dean wondered if her MBA graduates had similar experiences. She surveyed recent graduates from her​ school's MBA program to find that 24 ​% of the 115 graduates from the previous year claim to have encountered unethical business practices in the workplace What is the value of the test​ statistic? A. The assumptions and conditions are not​ met, so the test cannot proceed. B. The test statistic is nothing . ​(Round to two decimal places as​ needed.)

Answer 1

Solution:

Given: 27 ​% of newly hired MBAs are confronted with unethical business practices during their first year of employment.

Thus p = population proportion = 0.27

Sample size = n = 115

Sample proportion =

Claim: Newly hired MBAs are confronted with unethical business practices during their first year of employment is similar to stated proportion 27%.

This claim is non-directional thus this is two tailed test:

Thus hypothesis of the study are:

Vs

We have to find the value of the test​ statistic.

Since n * p = 115 * 0.27 = 31.05 > 10 and n*(1-p) = 115*(1-0.27) = 83.95 > 10 , both the conditions are met, we can use Normal approximation to proportion.

Thus we use z test statistic for proportion.

Find P-value:

P-value = 2 X P( Z < z test statistic )

P-value = 2 X P( Z < -0.72)

Look in z table for z = -0.7 and 0.02 and find corresponding area.

P( Z< -0.72) = 0.2358

thus

P-value = 2 X P( Z < -0.72)

P-value = 2 X 0.2358

P-value = 0.4716

P-value = 0.472

Since P-value = 0.472 > 0.05 significance level, we fail to reject null hypothesis H0.

Thus we get:

Fail to reject null hypothesis. There is insufficient evidence that the rate unethical business practices during their first year of employment is different from that reported in study.