Question

Create a 99% confidence interval for the mean using following data. Explain/show what you did to arrive are your answer.

x

10

20

90

50

20

30

40

10

80

10

Answer 1

Mean = X / n = 360 / 10 = 36

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

= sqrt [ (20600 - 10 * 362 ) / 9 ]

= 29.1357

99% Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.01 /2, 10- 1 ) = 3.25
36 ± 3.25 * 29.1357/√(10)
Lower Limit = 36 - 3.5 * 29.1357/√(10)
Lower Limit = 6.06
Upper Limit = 36 + 3.25 * 29.1357/√(10)
Upper Limit = 65.94
99% Confidence interval is ( 6.06 , 65.94 )