To assess how women are doing in the workforce, we have gathered data from 120 firms with 100 to 500 employees, and have recorded how many of the top 25 highest paid employees are female. Use the data provided in the image.Q1 What is the overall proportion of females in the top 25? Answer is .5093Q2 What is the lower bound of the 95% confidence interval for the mean proportion of females in the top 25?Answers are not: .4895 or .4634 or .0541 or .0550 or .0542Q3 What is the upper bound of the 95% confidence interval for the mean proportion of females in the top 25?Answers are not: .0020 or .6794 or .0597 or .0587 or .0746 or .0983 Firm123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120Total # of Employees170355233191191374318291106201106111355343160174169339288235236389128155242361226118301159113142360106199355211468204321355111146250249145160150176230192179302150105158143134106174224108175463161376270111212162119255155373287207167124212217393261222301242242222195213248305380275149154213212108122153179274260150260303184246303171420284210324244206113104139357# of Female in top 251510161218116161412181513111015141613129138101410111215712161261014171481113101917121110161818187811816142019161619151210411192010129121413713791315131212101215101441111131291311121210111810221111121513121310131212111315181218

Given: Sample size n = 120 Sample proportion p^ = 0.5093 Formula Used: Lower bound of the confidence…

Answered: To assess how women are doing in the…

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter33: Digital Calipers And Height Gages

Section: Chapter Questions

Problem 5A

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Question

To assess how women are doing in the workforce, we have gathered data from 120 firms with 100 to 500 employees, and have recorded how many of the top 25 highest paid employees are female. Use the data provided in the image.

Q1 What is the overall proportion of females in the top 25? Answer is .5093

Q2 What is the lower bound of the 95% confidence interval for the mean proportion of females in the top 25?

Answers are not: .4895 or .4634 or .0541 or .0550 or .0542

Q3 What is the upper bound of the 95% confidence interval for the mean proportion of females in the top 25?

Answers are not: .0020 or .6794 or .0597 or .0587 or .0746 or .0983

Firm
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
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49
50
51
52
53
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80
81
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83
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89
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92
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95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
Total # of Employees
170
355
233
191
191
374
318
291
106
201
106
111
355
343
160
174
169
339
288
235
236
389
128
155
242
361
226
118
301
159
113
142
360
106
199
355
211
468
204
321
355
111
146
250
249
145
160
150
176
230
192
179
302
150
105
158
143
134
106
174
224
108
175
463
161
376
270
111
212
162
119
255
155
373
287
207
167
124
212
217
393
261
222
301
242
242
222
195
213
248
305
380
275
149
154
213
212
108
122
153
179
274
260
150
260
303
184
246
303
171
420
284
210
324
244
206
113
104
139
357
# of Female in top 25
15
10
16
12
18
11
6
16
14
12
18
15
13
11
10
15
14
16
13
12
9
13
8
10
14
10
11
12
15
7
12
16
12
6
10
14
17
14
8
11
13
10
19
17
12
11
10
16
18
18
18
7
8
11
8
16
14
20
19
16
16
19
15
12
10
4
11
19
20
10
12
9
12
14
13
7
13
7
9
13
15
13
12
12
10
12
15
10
14
4
11
11
13
12
9
13
11
12
12
10
11
18
10
22
11
11
12
15
13
12
13
10
13
12
12
11
13
15
18
12
18

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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