Using the data below in Figure 1:Part Ayou tested a number of hypotheses about employees of your firm. Return to these data. Are your female and male employees significantly dif-ferent with respect to each of the following? Where necessary, assume population standard deviations are equal. Use α = 0.10. Use α = 0.05. What is the p-value of each test?a. Mean education?b. Mean job experience?c. Proportions employed in management?d. Mean salary?Part BFor which cases did you need to assume population standard deviations equal? Did the assumption seem tenable in these cases?Suppose you were unwilling to assume equal population standard deviations. How would your results change?Figure 1:IDEdExpTypeFemaleSalary1917433065.02011432048.72515423158.03014403149.93415392154.04210391040.94611361045.25210341041.65912343045.46913341148.87413331048.48214313049.88712312045.19214301045.39918282153.710511282040.510717263154.911015261049.811517253054.411711251038.912110252037.213017241054.113916231051.114016231149.114116231051.014910212131.715616201049.616411191036.316815191046.317317162148.718210132127.719116133046.119418121050.419911122033.220815113138.32171591041.32261392036.42341493038.92391361134.42401251032.22461232126.82491131124.02581432132.22671521134.82701321033.22771221030.42861011125.12901212029.92911412132.22921311032.4

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

Using the data below in Figure 1:

Part A

you tested a number of hypotheses about employees of your firm. Return to these data. Are your female and male employees significantly dif-ferent with respect to each of the following? Where necessary, assume population standard deviations are equal. Use α = 0.10. Use α = 0.05. What is the p-value of each test?

a. Mean education?

b. Mean job experience?

c. Proportions employed in management?

d. Mean salary?

Part B

For which cases did you need to assume population standard deviations equal? Did the assumption seem tenable in these cases?
Suppose you were unwilling to assume equal population standard deviations. How would your results change?

Figure 1:

ID	Ed	Exp	Type	Female	Salary
19	17	43	3	0	65.0
20	11	43	2	0	48.7
25	15	42	3	1	58.0
30	14	40	3	1	49.9
34	15	39	2	1	54.0
42	10	39	1	0	40.9
46	11	36	1	0	45.2
52	10	34	1	0	41.6
59	12	34	3	0	45.4
69	13	34	1	1	48.8
74	13	33	1	0	48.4
82	14	31	3	0	49.8
87	12	31	2	0	45.1
92	14	30	1	0	45.3
99	18	28	2	1	53.7
105	11	28	2	0	40.5
107	17	26	3	1	54.9
110	15	26	1	0	49.8
115	17	25	3	0	54.4
117	11	25	1	0	38.9
121	10	25	2	0	37.2
130	17	24	1	0	54.1
139	16	23	1	0	51.1
140	16	23	1	1	49.1
141	16	23	1	0	51.0
149	10	21	2	1	31.7
156	16	20	1	0	49.6
164	11	19	1	0	36.3
168	15	19	1	0	46.3
173	17	16	2	1	48.7
182	10	13	2	1	27.7
191	16	13	3	0	46.1
194	18	12	1	0	50.4
199	11	12	2	0	33.2
208	15	11	3	1	38.3
217	15	9	1	0	41.3
226	13	9	2	0	36.4
234	14	9	3	0	38.9
239	13	6	1	1	34.4
240	12	5	1	0	32.2
246	12	3	2	1	26.8
249	11	3	1	1	24.0
258	14	3	2	1	32.2
267	15	2	1	1	34.8
270	13	2	1	0	33.2
277	12	2	1	0	30.4
286	10	1	1	1	25.1
290	12	1	2	0	29.9
291	14	1	2	1	32.2
292	13	1	1	0	32.4

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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