Question

construct a 98 percent confidence interval from the data.

0.53 0.69 0.09 1.26 0.58 0.82

i would really apprecite it if someone explained how you find the standard deviation since im having trouble on that part.

Answer 1

From given data ,

= X / n = 3.97 / 6 = 0.6617

S = sqrt [ X2 - n 2 / ( n - 1) ]

= sqrt [ (3.3615 - 6 * 0.66172 ) / 5 ]

= 0.3833

98% Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.02 /2, 6- 1 ) = 3.365
0.6617 ± t(0.02/2, 6 -1) * 0.3833/√(6)
Lower Limit = 0.6617 - t(0.02/2, 6 -1) 0.3833/√(6)
Lower Limit = 0.135
Upper Limit = 0.6617 + t(0.02/2, 6 -1) 0.3833/√(6)
Upper Limit = 1.188
98% Confidence interval is ( 0.135 , 1.188 )