45 56 55 49 43 34 42 35 60 48 42 50 45 52 33 34 60 52 60 60 32 56 39 46 34 55 41
ID: 2956109 • Letter: 4
Question
45
56
55
49
43
34
42
35
60
48
42
50
45
52
33
34
60
52
60
60
32
56
39
46
34
55
41
59
41
50
40
44
60
49
63
80
52
22
80
72
56
70
56
24
46
70
74
70
61
65
71
39
74
79
76
71
49
62
68
71
67
69
45
(Points :6)
6. Given a level of confidence of 95% and a population standard deviation of 7, what other information is necessary:
(A) To find the Maximum Error of Estimate (E)?
(B) To find the sample size (n)?
(C) Given the above confidence level and population standard deviation, find the Maximum Error of Estimate (E) if n = 45. Show all your calculations. Show all work.
(D) For this same sample of n = 45, what is the width of the confidence interval around the population mean? Show all work.
(E) Given this same confidence level and standard deviation, find n if E = 3.0. (Always round to the nearest whole person.) Show all work.
(Points :10)
45
56
55
49
43
34
42
35
60
48
42
50
45
52
33
34
60
52
60
60
32
56
39
46
34
55
41
59
41
50
40
44
60
Explanation / Answer
We have sample size n = 25, mean = 75 & Std Dev =6a. For 95% COnf Level, a = 0.05
So area under the curve is 1-0.05 = 0.95. So area to right of Mean is 0.95/2 = 0.475.
Looking at z-table for 0.475, we find z = 1.96 for which area under the curve is 0.475
we have given data n = 25 & Std Dev s = 6, Mean µ= 75
So Sample Std dev s = s/vn = 6/v25 =1.2
Margin of Error E is given by E = s* z = 1.2*1.96 = 2.352
So Interval estimates are µ± E = 75 ± 2.352
SO Interval est are 72.648 & 77.353 ......Ans b. For 95% COnf Level, a = 0.05
So area under the curve is 1-0.05 = 0.95. So area to right of Mean is 0.95/2 = 0.475.
Looking at z-table for 0.475, we find z = 1.96 for which area under the curve is 0.475
we have given data n = 36 & Std Dev s = 6, Mean µ= 75
So Sample Std dev s = s/vn = 6/v36 =1
Margin of Error E is given by E = s* z = 1*1.96 = 1.96
So Interval estimates are µ± E = 75 ± 1.96
SO Interval est are 73.04 & 76.96 ......Ans c. COnfidence interval with sample size of 36 is smaller. A sample size of a statistical sample is the number of observations that constitute it. It is typically denoted by 'n', a positive integer (natural number).
Typically, all else being equal, a larger sample size leads to increased precision in estimates of various properties of the population. Hence when sample size increases from 25 to 36, the MoE become more precise & reduces from 2.352 to 1.96
a. For 95% COnf Level, a = 0.05
So area under the curve is 1-0.05 = 0.95. So area to right of Mean is 0.95/2 = 0.475.
Looking at z-table for 0.475, we find z = 1.96 for which area under the curve is 0.475
we have given data n = 25 & Std Dev s = 6, Mean µ= 75
So Sample Std dev s = s/vn = 6/v25 =1.2
Margin of Error E is given by E = s* z = 1.2*1.96 = 2.352
So Interval estimates are µ± E = 75 ± 2.352
SO Interval est are 72.648 & 77.353 ......Ans b. For 95% COnf Level, a = 0.05
So area under the curve is 1-0.05 = 0.95. So area to right of Mean is 0.95/2 = 0.475.
Looking at z-table for 0.475, we find z = 1.96 for which area under the curve is 0.475
we have given data n = 36 & Std Dev s = 6, Mean µ= 75
So Sample Std dev s = s/vn = 6/v36 =1
Margin of Error E is given by E = s* z = 1*1.96 = 1.96
So Interval estimates are µ± E = 75 ± 1.96
SO Interval est are 73.04 & 76.96 ......Ans b. For 95% COnf Level, a = 0.05
So area under the curve is 1-0.05 = 0.95. So area to right of Mean is 0.95/2 = 0.475.
Looking at z-table for 0.475, we find z = 1.96 for which area under the curve is 0.475
we have given data n = 36 & Std Dev s = 6, Mean µ= 75
So Sample Std dev s = s/vn = 6/v36 =1
Margin of Error E is given by E = s* z = 1*1.96 = 1.96
So Interval estimates are µ± E = 75 ± 1.96
SO Interval est are 73.04 & 76.96 ......Ans c. COnfidence interval with sample size of 36 is smaller. A sample size of a statistical sample is the number of observations that constitute it. It is typically denoted by 'n', a positive integer (natural number).
Typically, all else being equal, a larger sample size leads to increased precision in estimates of various properties of the population. Hence when sample size increases from 25 to 36, the MoE become more precise & reduces from 2.352 to 1.96
A sample size of a statistical sample is the number of observations that constitute it. It is typically denoted by 'n', a positive integer (natural number).
Typically, all else being equal, a larger sample size leads to increased precision in estimates of various properties of the population. Hence when sample size increases from 25 to 36, the MoE become more precise & reduces from 2.352 to 1.96
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