Question

In: Statistics and Probability

Person Gender Generation Millennial Gen X Younger Boomer Older Boomer Silent GI Facebook Twitter Pinterest Linkedin...

Person Gender Generation
Millennial
Gen X
Younger Boomer
Older Boomer
Silent
GI		 Facebook Twitter Pinterest Linkedin Snapchat Landline Text Message email Letters Desktop
or
Laptop		 Tablet Smartphone # of text messages sent yesterday
Example Female Millennial Yes Yes No No No No Yes Yes No 2 3 3 20
Example Male Gen X Yes No No Yes No Yes No Yes Yes 5 1 5 5
1 Male Millennial Yes Yes No No No Yes No No Yes 3 1 3 26
2 Female Millennial Yes Yes Yes Yes Yes No Yes No Yes 4 3 1 58
3 Female Gen X Yes No No Yes No Yes No No No 1 2 2 61
4 Female Gen X Yes No Yes Yes No No Yes Yes Yes 2 3 1 45
5 Male Gen X Yes No No Yes Yes No Yes No Yes 4 2 4 90
6 Female Gen X No Yes No No No No Yes No No 3 2 0 17
7 Female Millennial Yes No No No No No Yes Yes No 0 4 2 6
8 Male Millennial Yes Yes No No Yes Yes No Yes Yes 0 0 0 25
9 Female Millennial Yes No No Yes Yes Yes No No No 1 1 0 38
10 Male Millennial No Yes No Yes No Yes Yes Yes No 4 4 4 12
11 Female Millennial Yes No Yes No Yes No No No Yes 2 1 2 98
12 Female Younger Boomer No Yes Yes No Yes Yes Yes No Yes 4 3 3 6
13 Female Younger Boomer No No Yes Yes Yes No Yes Yes Yes 3 4 4 38
14 Female Millennial Yes Yes No No No No Yes No No 2 4 2 95
15 Male Millennial No Yes No Yes No No Yes No Yes 4 1 1 84
16 Male Millennial No Yes Yes Yes Yes No No Yes Yes 1 2 3 41
17 Female Older Boomer No Yes No Yes No Yes Yes Yes Yes 3 2 4 87
18 Female Millennial No No Yes Yes No Yes Yes Yes No 2 2 4 84
19 Female Millennial Yes No No No No No No Yes Yes 4 1 2 33
20 Female Gen X No Yes No No No Yes No Yes Yes 0 1 0 27
21 Female Millennial Yes No Yes Yes Yes Yes No Yes Yes 2 0 0 63
22 Male Older Boomer No Yes Yes Yes Yes No Yes Yes Yes 3 0 2 26
23 Female Older Boomer No No Yes No Yes Yes Yes No Yes 3 0 1 80
24 Male Millennial Yes Yes No Yes No Yes No No Yes 3 0 2 4
25 Male Younger Boomer Yes No Yes No Yes No Yes No Yes 2 2 1 18
26 Male Millennial No No No No Yes No Yes Yes Yes 3 4 4 20
27 Male Younger Boomer No Yes Yes No No Yes Yes No No 3 2 3 89
28 Female Millennial No Yes No Yes Yes Yes No Yes Yes 1 2 3 6
29 Male Millennial No No Yes Yes No Yes No Yes No 0 1 2 94
30 Male Millennial Yes Yes Yes No Yes No Yes No No 3 1 1 98
31 Female Younger Boomer No No Yes Yes Yes No No Yes Yes 4 3 4 33
32 Female Millennial No Yes Yes No No No No No Yes 4 2 4 57
33 Male Younger Boomer No Yes No No No No No No Yes 1 3 2 25
34 Male Gen X Yes No No No Yes Yes No Yes No 3 3 0 41
35 Female Millennial Yes Yes No No Yes Yes Yes Yes No 0 1 1 57
36 Female Millennial Yes No No No Yes No No Yes No 4 0 4 71
37 Female Millennial No No No No Yes Yes Yes Yes Yes 4 4 4 96
38 Female Millennial Yes No No No No No Yes Yes Yes 0 1 0 22
39 Male Millennial No Yes No Yes Yes No No Yes No 1 0 3 61
40 Male Millennial Yes No No Yes Yes Yes No No No 2 3 3 16
41 Male Millennial Yes No No Yes No Yes Yes No Yes 4 4 2 24
42 Female Millennial Yes No No No No No No Yes Yes 0 4 3 40
43 Male Millennial No No No No Yes No No Yes Yes 1 3 2 29
44 Male Millennial No Yes No Yes Yes Yes No Yes Yes 0 1 3 30
45 Female Millennial No Yes No Yes Yes Yes No Yes No 1 3 3 54
46 Male Millennial No Yes No No No No No No Yes 2 4 1 73
47 Female Millennial No Yes Yes No Yes Yes Yes No Yes 4 1 0 48
48 Male Millennial Yes No Yes Yes No No Yes No Yes 1 1 0 84
49 Female Younger Boomer No No No No Yes Yes Yes Yes No 3 1 4 93
50 Female Gi Yes Yes Yes Yes Yes No Yes Yes No 2 2 0 14
  1. Using LinkedIn data, calculate 95% confidence interval for the population proportion that use linkedin.
  2. Using Facebook data calculate 90% confidence interval for the population proportion that use Facebook

Solutions

Expert Solution

Solution

Back-up Theory

100(1 - α) % Confidence Interval for the population proportion, p is:

phat ± MoE, …………………………………........………………………………. (1)

where

MoE = Zα/2[√{phat (1 – phat)/n}] …………………………………....…………..(2)

with

Zα/2 is the upper (α/2)% point of N(0, 1),

phat = sample proportion, and

n = sample size.

Now, to work out the solution,

95% Confidence Interval for the population proportion that use linkedin is: [0.34 < p < 0.62] Answer 1

Details of calculations

n

50

X

24

p' = phat

0.48

F = p'(1-p')/n

0.004992

sqrtF

0.070654

α

0.05

1 - (α/2)

0.975

Zα/2

1.959964

MoE

0.138479

LB

0.341521

UB

0.618479

90% Confidence Interval for the population proportion that use Facebook is: [0.36 < p < 0.60] Answer 2

Details of calculations

n

50

X

24

p' = phat

0.48

F = p'(1-p')/n

0.004992

sqrtF

0.070654

α

0.1

1 - (α/2)

0.95

Zα/2

1.644854

MoE

0.116216

LB

0.363784

UB

0.596216

DONE

orchestra answered 3 years ago
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