Question

One study reports that 34​% 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 31​% of the 129 graduates from the previous year claim to have encountered unethical business practices in the workplace. Can she conclude that her​ graduates' experiences are​ different?

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? ​(Round to two decimal places as​ needed.)

What is P-value of the test statistic?

A. P-value? (Round to three decimal places as​ needed.)

B. The assumptions and conditions are not​ met, so the test cannot proceed.

Answer 1

Solution :

Assumptions and conditions :

n = 129 and p_{​​​​​​0} = 0.34

Because np_​​​0(1 - p_{​​​​​​0}) = 28.9476, which is greater than 10, the sample size is less than 5% of the population size and the sample can be reasonably assumed to be random, therefore the assumptions and conditions are met.

Null and alternative hypotheses :

The null and alternative hypotheses would be as follows :

Test statistic :

To test the hypothesis the most appropriate test is one proportion z-test. The test statistic is given as follows :

Where, p̂ is sample proportion, p is hypothesized value of population proportion under H_{​​​​​​0}, q = 1 - p and n is sample size.

Sample proportion of graduates from the previous year who claim to have encountered unethical business practices in the workplace is, p̂ = 31% = 0.31.

n = 129, p = 34% = 0.34 and q = (1 - 0.34) = 0.66

The value of the test statistic is z = -0.72

P-value :

Since, our test is two-tailed test, therefore we shall obtain two-tailed p-value for the test statistic. The two-tailed p-value is given as follows :

P-value = 2.P(Z > |z|)

We have, |z| = 0.72

P-value = 2.P(Z > 0.72)

P-value = 0.472

The p-value is 0.472.

Decision :

In our question significance level is not given. Generally significance level of 0.05 or 0.01 is used. We shall significance level of 0.01.

Significance Level = 0.01

P-value = 0.472

(0.472 > 0.01)

Since, p-value is greater than the significance level of 0.01, therefore we shall be fail to reject the null hypothesis (H_{​​​​​​0}) at 0.01 significance level.

Conclusion :

At 0.01 significance level, there is not sufficient evidence to conclude that her​ graduate's students experiences are​ different.

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