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Ashford 5: - Week 4 - Discussion 1

Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Reference the Discussion Forum Grading Rubric for guidance on how your discussion will be evaluated.

Confidence Intervals

Many people do not “like” or “trust” single point estimates for things they need measured. Looking back at the data examples you have provided in the previous discussion questions on this issue, how might adding confidence intervals help managers accept the results better? Why?

Ask a manger in your organization if they would prefer a single point estimate or a range for important measures, and why? Please share what they say. Guided Response: Review several of your classmates’ posts. Respond to at least two classmates by commenting on whether or not you think adding or using confidence intervals would result in greater acceptance. Explain if you agree or disagree with the role of a confidence interval in the interpretation of the answer.

Ashford 5: - Week 4 - Discussion 2

Chi-Square Tests

Chi-square tests are great to show if distributions differ or if two variables interact in producing outcomes. What are some examples of variables that you might want to check using the chi-square tests? What would these results tell you?

Guided Response: Review several of your classmates’ posts. Respond to at least two classmates by commenting on how this information might be used to make business decisions.

See comments at the right of the data set.
ID	Salary	Compa	Midpoint	Age	Performance Rating	Service	Gender	Raise	Degree	Gender1	Grade
8	23	1.000	23	32	90	9	1	5.8	0	F	A	The ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)?
10	22	0.956	23	30	80	7	1	4.7	0	F	A	Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
11	23	1.000	23	41	100	19	1	4.8	0	F	A
14	24	1.043	23	32	90	12	1	6	0	F	A	The column labels in the table mean:
15	24	1.043	23	32	80	8	1	4.9	0	F	A	ID – Employee sample number	Salary – Salary in thousands
23	23	1.000	23	36	65	6	1	3.3	1	F	A	Age – Age in years		Performance Rating – Appraisal rating (Employee evaluation score)
26	24	1.043	23	22	95	2	1	6.2	1	F	A	Service – Years of service (rounded)	Gender: 0 = male, 1 = female
31	24	1.043	23	29	60	4	1	3.9	0	F	A	Midpoint – salary grade midpoint	Raise – percent of last raise
35	24	1.043	23	23	90	4	1	5.3	1	F	A	Grade – job/pay grade	Degree (0= BS\BA 1 = MS)
36	23	1.000	23	27	75	3	1	4.3	1	F	A	Gender1 (Male or Female)	Compa - salary divided by midpoint
37	22	0.956	23	22	95	2	1	6.2	1	F	A
42	24	1.043	23	32	100	8	1	5.7	0	F	A
3	34	1.096	31	30	75	5	1	3.6	0	F	B
18	36	1.161	31	31	80	11	1	5.6	1	F	B
20	34	1.096	31	44	70	16	1	4.8	1	F	B
39	35	1.129	31	27	90	6	1	5.5	1	F	B
7	41	1.025	40	32	100	8	1	5.7	0	F	C
13	42	1.050	40	30	100	2	1	4.7	1	F	C
22	57	1.187	48	48	65	6	1	3.8	0	F	D
24	50	1.041	48	30	75	9	1	3.8	1	F	D
45	55	1.145	48	36	95	8	1	5.2	0	F	D
17	69	1.210	57	27	55	3	1	3	0	F	E
48	65	1.140	57	34	90	11	1	5.3	1	F	E
28	75	1.119	67	44	95	9	1	4.4	1	F	F
43	77	1.149	67	42	95	20	1	5.5	1	F	F
19	24	1.043	23	32	85	1	0	4.6	1	M	A
25	24	1.043	23	41	70	4	0	4	0	M	A
40	25	1.086	23	24	90	2	0	6.3	0	M	A
2	27	0.870	31	52	80	7	0	3.9	0	M	B
32	28	0.903	31	25	95	4	0	5.6	0	M	B
34	28	0.903	31	26	80	2	0	4.9	1	M	B
16	47	1.175	40	44	90	4	0	5.7	0	M	C
27	40	1.000	40	35	80	7	0	3.9	1	M	C
41	43	1.075	40	25	80	5	0	4.3	0	M	C
5	47	0.979	48	36	90	16	0	5.7	1	M	D
30	49	1.020	48	45	90	18	0	4.3	0	M	D
1	58	1.017	57	34	85	8	0	5.7	0	M	E
4	66	1.157	57	42	100	16	0	5.5	1	M	E
12	60	1.052	57	52	95	22	0	4.5	0	M	E
33	64	1.122	57	35	90	9	0	5.5	1	M	E
38	56	0.982	57	45	95	11	0	4.5	0	M	E
44	60	1.052	57	45	90	16	0	5.2	1	M	E
46	65	1.140	57	39	75	20	0	3.9	1	M	E
47	62	1.087	57	37	95	5	0	5.5	1	M	E
49	60	1.052	57	41	95	21	0	6.6	0	M	E
50	66	1.157	57	38	80	12	0	4.6	0	M	E
6	76	1.134	67	36	70	12	0	4.5	1	M	F
9	77	1.149	67	49	100	10	0	4	1	M	F
21	76	1.134	67	43	95	13	0	6.3	1	M	F
29	72	1.074	67	52	95	5	0	5.4	0	M	F

Score:

Week 4

Confidence Intervals and Chi Square (Chs 11 - 12)

For questions 3 and 4 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your

decisions.

For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed.

<1 point>

Using our sample data, construct a 95% confidence interval for the population's mean salary for each gender.

Interpret the results. How do they compare with the findings in the week 2 one sample t-test outcomes (Question 1)?

Mean

St error

t value

Low

High

Males

Females

<Reminder: standard error is the sample standard deviation divided by the square root of the sample size.>

Interpretation:

<1 point>

Using our sample data, construct a 95% confidence interval for the mean salary difference between the genders in the population.

How does this compare to the findings in week 2, question 2?

Difference

St Err.

T value

Low

High

Yes/No

Can the means be equal?

Why?

How does this compare to the week 2, question 2 result (2 sampe t-test)?

Why is using a two sample tool (t-test, confidence interval) a better choice than using 2 one-

sample techniques when comparing two samples?

<1 point>

We found last week that the degree values within the population do not impact compa rates.

This does not mean that degrees are distributed evenly across the grades and genders.

Do males and females have athe same distribution of degrees by grade?

(Note: while technically the sample size might not be large enough to

perform this test, ignore this limitation for this exercise.)

What are the hypothesis statements:

Ho:

Ha:

Note: You can either use the Excel Chi-related functions or do the calculations manually.

Data input tables - graduate degrees by gender and grade level

OBSERVED

Total

If desired, you can do manual calculations per cell here.

M Grad

Fem Grad

M Grad

Male Und

Fem Grad

Female Und

Male Und

Female Und

Sum =

EXPECTED

M Grad

For this exercise - ignore the requirement for a correction factor

Fem Grad

for cells with expected values less than 5.

Male Und

Female Und

Interpretation:

What is the value of the

chi square statistic:

What is the p-value

associated with this value:

Is the p-value <0.05?

Do you reject or not reject

the null hypothesis:

If you rejected the null,

what is the Cramer's V

correlation:

What does this correlation mean?

What does this decision

mean for our equal pay question:

<1 point>

Based on our sample data, can we conclude that males and females are distributed across

grades in a similar pattern

within the population?

What are the hypothesis statements:

Ho:

Ha:

Do manual calculations per cell here (if desired)

OBS COUNT - m

OBS COUNT - f

Sum =

EXPECTED

What is the value of the

chi square statistic:

What is the p-value

associated with this value:

Is the p-value <0.05?

Do you reject or not

reject the null hypothesis:

If you rejected the null,

what is the Phi correlation:

What does this correlation mean?

What does this decision

mean for our equal pay question:

<2 points>

5. How do you interpret these results in light of our question about equal pay for equal work?