In: Statistics and Probability
Person | Gender | Generation Millennial Gen X Younger Boomer Older Boomer Silent GI |
Snapchat | Landline | Text Message | 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 |
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