Based on this data: 4a. Do a hypothesis test to determine if the proportion of f

Question

Based on this data:

4a. Do a hypothesis test to determine if the proportion of females that make less than $38000 is more than the proportion of males that make less than $38000. Use = .01 and make sure to show ALL steps of the hypothesis test and include both the critical value AND p-value approaches. Show all work. Show your hypothesis test below. (10 points) b. Does this hypothesis test suggest gender discrimination? Why or why not? (2 points) The following agreements were presented in the lawsuit. 5a. POINT of the Lawsuit: Management presents their case as two independent means. Conduct a hypothesis test to test the following claim: "The mean pay of the female managers is less than their male counterparts." At the 0.05 level of significance, test whether the following corporation is guilty of "gender discrimination" in the manner they pay their employees. and make sure to show ALL steps of the hypothesis test and include both the critical value AND p-value approaches. Show all work. Show your hypothesis test below. (10 points)

b. Using this hypothesis test can it be concluded that there is gender discrimination? Why or why not? (2 points)

6. COUNTERPOINT of the Lawsuit: Labor presents their case as two dependent means. Every effort was made in pairing the data (same amount of experience, same responsibilities, etc.).

a. You must find the difference in pay for each pair of employees (each male is paired with a female). For example the first female value is 43800 and its paired male value is 44000 and the difference is: 43800 – 44000 = -200. -200 should be the data value you are using. Find the mean of the differences and the standard deviation of the differences, rounded to two decimal places. (2 points) Differences: D = sD =

b. Using the case of two dependent means, conduct a hypothesis test to test the following claim:"The mean pay of the female managers is less than their male counterparts." At the 0.05 level of significance, test whether the following corporation is guilty of "gender discrimination" in the manner they pay their employees. Make sure to show ALL steps of the hypothesis test and include both the critical value AND p-value approaches. Show all work. Show your hypothesis test below. (10 points)

c. Using this hypothesis test can it be concluded that there is gender discrimination? Why or why not? (2 points)

7. Which approach – point or counterpoint - should the jury believe? Explain. Make sure to consider dependent vs independent samples. Can the confidence interval of female salaries, the confidence interval of male salaries, the hypothesis test that males earn more than $36,500 a year, and the hypothesis test on proportions help the case? Explain. (5 points)

males females 44000 36500 36000 38000 38000 39700 42000 35500 37000 43800 35000 33000 56000 54000 36000 36000 53000 54000 36000 35500 38000 34900 38000 36900 50000 47800 45500 42000 31000 30000 41500 42000 38500 39000 42000 42500 31000 31000 39500 38000

Explanation / Answer

Solution

Let p1 and p2 represent the population proportion of male and female employees respectively who make less than $38000.

Let p1cap and p2cap represent the sample proportion of males and females respectively who make less than $38000.

Let n1 and n2 be the respective sample sizes.[In the present case n1 = n2 = n, say, = 20]

Q4 Part (a)

Claim: Proportion of female employees who make less than $38000 is more than proportion of male employees who make less than $38000.

Hypotheses:

Null H0: p1 = p2   Vs

Alternative HA: p2 > p1 [claim]

Test statistic:

Z = (p2 – p1)/sqrt[pcap(1 - pcap)(2/n), where pcap = (p1cap + p2cap)/2

Calculations

By Excel sorting, p1cap = 7/20 = 0.35 and p2cap = 9/20 = 0.45

So, pcap = 0.40, and

Z = 0.1/sqrt(0.4 x 0.6 x 0.1) = 0.645

Distribution, Critical Value and p-value

Under H0, Z ~ N(0, 1)

Critical value = upper % point of N(0, 1).

p-value = P(Z > 0.645) = 0.2595 [using Excel Function]

Given = 0.01, Zcrit = 2.326 [using Excel Function]

Decision Criterion (Rejection Region)

Reject H0, if Zcal > Zcrit or p-value < .

Decision:

Since Zcal < Zcrit, H0 is accepted.

Since p-value > H0 is accepted.

Conclusion:

There is not sufficient evidence to support the claim that proportion of female employees who make less than $38000 is more than proportion of male employees who make less than $38000.

DONE

Q4Part (b)

Since hypothesis testing does not give evidence to validate the claim, it is only fair to assume that there is no gender discrimination.ANSWER

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