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

Answer:

68% Confidence interval  = [4.5752, 4.5848]

95% Confidence interval  = [4.5688, 4.5918]

Step-by-step 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 = $[x-T_{(5)}\frac{S}{\sqrt{n}}, x+T_{(5)]\frac{S}{\sqrt{n}}]$ = [4.5752, 4.5848]

95% Confidence interval = $[x-T_{(5)}\frac{S}{\sqrt{n}}, x+T_{(5)}\frac{S}{\sqrt{n}}]$ = [4.5688, 4.5918]