A sample of n 26 observations are taken from a normal popul

A sample of n = 26 observations are taken from a normal population with unknown mean and variance. From the sample we have:

A.) Suppose an additional 3 observations are taken, x₂₇ = 260, x₂₈ = 392, and x₂₉ = 384. Calculate the new sample mean and sample standard deviation.

B.) Using the information in (A.), construct a 99% two-sided confidence interval for the population mean.

Solution

Sum of 26 items = 9637.90

Add 3 information = 260+392+384

Grand total = 10673.90

New sample mean = 10673.9/29 =368.065

Sum of x^2 = 2858750

Add square of three new items = 67600+153664+147456=368720

E(X^2) =3227470/29 = 111292.069

Var(x) = 111292.069-368.065^2=

AS variance is negative there is some mistake in the data.