I need the answers 4 through 7 please manual answers. No excel answers please. I
ID: 3267172 • Letter: I
Question
I need the answers 4 through 7 please manual answers. No excel answers please. I do have already answer 1 to 3 Thank you
Suppose the following data represents the annual salaries of twenty male and female managers. The data is not real.
Female
Male
Female
Male
Female
Male
Female
Male
$43,800
$44,000
$33,000
$35,000
$34,900
$38,000
$42,000
$41,500
$35,500
$36,000
$54,000
$56,000
$36,900
$38,000
$39,000
$38,500
$39,700
$38,000
$36,000
$36,000
$47,800
$50,000
$42,500
$42,000
$38,000
$42,000
$54,000
$53,000
$42,000
$45,500
$31,000
$31,000
$36,500
$37,000
$35,500
$36,000
$30,000
$31,000
$38,000
$39,500
1. Using your calculator or excel, find the sample mean and sample standard deviation, rounded to two decimal places, for both females and males. You may check these values with your instructor before continuing. Each re-attempt will result in a lost point. (2 points)
Females: = s = Males: = s =
2. We will now gather some basic information that may help us in the case.
a. For Females, find a 95% confidence interval of the average annual salaries of managers. Show all work. Interpret your results. (6.5 points)
b. For Males, find a 95% confidence interval of the average annual salaries of managers. Show all work. Interpret your results. (6.5 points)
3a. For Males, test the claim that male managers earn more than $36,500 a year. (36,500 is the approximate value of the low value for the confidence interval done above for females above) Use a .025 level of significance 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)
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. (See example on page 546) You may check these values with your instructor before continuing. Each re-attempt will result in a lost point. (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
Female
Male
Female
Male
Female
Male
Female
Male
$43,800
$44,000
$33,000
$35,000
$34,900
$38,000
$42,000
$41,500
$35,500
$36,000
$54,000
$56,000
$36,900
$38,000
$39,000
$38,500
$39,700
$38,000
$36,000
$36,000
$47,800
$50,000
$42,500
$42,000
$38,000
$42,000
$54,000
$53,000
$42,000
$45,500
$31,000
$31,000
$36,500
$37,000
$35,500
$36,000
$30,000
$31,000
$38,000
$39,500
Explanation / Answer
4. a
Null Hypothesis H0 : The proportion of females that make less than $38000 is equal to the proportion of males that make less than $38000.
Alternative Hypothesis H1 : The proportion of females that make less than $38000 is more than the proportion of males that make less than $38000.
Proportion of female with salary less than $38,000 = 9/20 = 0.45
Proportion of male with salary less than $38,000 = 7/20 = 0.35
Pooled Sample Proportion, p = (p1 * n1 + p2 * n2) / (n1 + n2)
= (0.45*20 + 0.35*20) / (20+20) = 0.4
Standard error (SE) of the sampling distribution difference between two proportions.
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] } = sqrt{ 0.4 * ( 1 - 0.4 ) * [ (1/20) + (1/20) ] } = 0.155
The test statistic is a z-score (z) defined by the following equation.
z = (p1 - p2) / SE
z = (0.45 - 0.35)/ 0.155 = 0.6452
p-value for z = 0.6452 is 0.2594
As, p-value is less than the significance level of 0.01, we fail to reject the null hypothesis.
4. b
As, we fail to reject the null hypothesis, we conclude that there is not enough data to prove that the proportion of females that make less than $38000 is more than the proportion of males that make less than $38000. So, this hypothesis test does not suggest gender discrimination
5. a
Null Hypothesis H0 : The mean pay of the female managers is equal to their male counterparts.
Alternative Hypothesis H1 : The mean pay of the female managers is less than their male counterparts.
Mean pay of the female managers = 39505
Mean pay of the male managers = 40400
Standard deviation of the pay of the female managers, s1 = 6569.825
Standard deviation of the pay of the male managers, s2 = 6636.423
Standard error (SE) of the sampling distribution, SE = sqrt[ (s12/n1) + (s22/n2) ]
SE = sqrt[ (6569.8252/20) + (6636.4232/20) ] = 2088.118
Degrees of freedom. The degrees of freedom (DF) is:
DF = (6569.8252/20 + 6636.4232/20)2 / { [ (6569.8252 / 20)2 / (20 - 1) ] + [ (6636.4232 / 20)2 / (20 - 1) ] }
= 38
Test statistic, t = (39505 - 40400) / 2088.118 = - 0.4286
p-value at t = -0.4286 and df = 38 is 0.3353 which is greater than the significance level of 0.05.
Also, critical value of t at significance level of 0.05 and df = 38 is -1.68
As, observed t is greater than the critical value (-1.68), we fail to reject the null hypothesis.
5 b.
As, we fail to reject the null hypothesis, we conclude that there is not enough data to prove that the mean pay of the female managers is less than their male counterparts. So, this hypothesis test does not suggest gender discrimination.