Question
Use ? to approximate σ. Use a 5% level of significance. Data: 69 62 75 66...
Use ? to approximate σ. Use a 5% level of significance.
Data:
69
62
75
66
68
57
61
84
61
77
62
71
68
69
79
76
87
78
73
89
81
73
64
65
73
69
57
79
78
80
79
81
73
74
84
83
82
85
86
77
72
79
59
64
65
82
64
70
83
89
69
73
84
76
79
81
80
74
77
66
68
77
79
78
77
Homework Answers
Answer #1
The given data is inputted in EXCEL and the following computations are made to obtain the sample standard deviation here:
| X | (X - Mean(X))^2 | |
| 69 | 26.56213018 | |
| 62 | 147.7159763 | |
| 75 | 0.715976331 | |
| 66 | 66.4852071 | |
| 68 | 37.86982249 | |
| 57 | 294.2544379 | |
| 61 | 173.0236686 | |
| 84 | 96.94674556 | |
| 61 | 173.0236686 | |
| 77 | 8.100591716 | |
| 62 | 147.7159763 | |
| 71 | 9.946745562 | |
| 68 | 37.86982249 | |
| 69 | 26.56213018 | |
| 79 | 23.4852071 | |
| 76 | 3.408284024 | |
| 87 | 165.0236686 | |
| 78 | 14.79289941 | |
| 73 | 1.331360947 | |
| 89 | 220.408284 | |
| 81 | 46.86982249 | |
| 73 | 1.331360947 | |
| 64 | 103.1005917 | |
| 65 | 83.79289941 | |
| 73 | 1.331360947 | |
| 69 | 26.56213018 | |
| 57 | 294.2544379 | |
| 79 | 23.4852071 | |
| 78 | 14.79289941 | |
| 80 | 34.17751479 | |
| 79 | 23.4852071 | |
| 81 | 46.86982249 | |
| 73 | 1.331360947 | |
| 74 | 0.023668639 | |
| 84 | 96.94674556 | |
| 83 | 78.25443787 | |
| 82 | 61.56213018 | |
| 85 | 117.6390533 | |
| 86 | 140.3313609 | |
| 77 | 8.100591716 | |
| 72 | 4.639053254 | |
| 79 | 23.4852071 | |
| 59 | 229.6390533 | |
| 64 | 103.1005917 | |
| 65 | 83.79289941 | |
| 82 | 61.56213018 | |
| 64 | 103.1005917 | |
| 70 | 17.25443787 | |
| 83 | 78.25443787 | |
| 89 | 220.408284 | |
| 69 | 26.56213018 | |
| 73 | 1.331360947 | |
| 84 | 96.94674556 | |
| 76 | 3.408284024 | |
| 79 | 23.4852071 | |
| 81 | 46.86982249 | |
| 80 | 34.17751479 | |
| 74 | 0.023668639 | |
| 77 | 8.100591716 | |
| 66 | 66.4852071 | |
| 68 | 37.86982249 | |
| 77 | 8.100591716 | |
| 79 | 23.4852071 | |
| 78 | 14.79289941 | |
| 77 | 8.100591716 | |
| 4820 | 4204.461538 |
The sample mean here is computed as:
Now the sample standard deviation here is computed as:
For n - 1 = 64 degrees of freedom, we have from chi square
distribution tables:
Also, we have here:
Therefore, 
Therefore the 95% confidence interval for population standard deviation here is computed as:
this is the required 95% confidence interval for the population standard deviation here.
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