Question

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

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.