Question

calculate the means and the standard deviation of the following set of data 4.578g, 4.581g, 4.572g, 4.573g, 4.601g, 4.577g. state the 68% and 95% confidence intervals for this data

Answer 1

68% Confidence interval = [4.5752, 4.5848]

95% Confidence interval = [4.5688, 4.5918]

Explanation:

Sample mean (X) = 4.580

Sample Standard Deviation (S) = 0.01065

Sample size (n) = 6

`T_((5))` for alpha/2 0.84 = 1.1037

`T_((5))` for alpha/2 0.975 = 2.5706

68% Confidence interval =
`[x-T_((5))(S)/(√(n)), x+T_{(5)](S)/(√(n))]` = [4.5752, 4.5848]

95% Confidence interval =
`[x-T_((5))(S)/(√(n)), x+T_((5))(S)/(√(n))]` = [4.5688, 4.5918]