A geologist is making repeated measurements in grams on the

A geologist is making repeated measurements (in grams) on the mass of a rock. It is not known whether the measurements are a random sample from an approximately normal population. Below are two sets of replicate measurements, listed in the order they were made. a. 213.03 212.95 213.04 213.00 212.99 213.01 221.03 213.05 b. 213.05 213.00 212.94 213.09 212.98 213.02 213.06 212.99 State which data set is more normally distributed and why the other one isn?t? And then find a p-value range for H0 : mu=213 and H1 : mu not equal to 213 for data set (a).

Solution

Set a is more normally distribution because one outlier is more closed to the mean.

sample mean=214.0125

sample standard deviation =2.835675

sample size=8

The test statistic is

t=(xbar-mu)/(s/vn)

=(214.0125-213)/(2.835675/sqrt(8))

=1.01

The degree of freedom =n-1=8-1=7

It is a two-tailed test.

So the p-value= 2*P(t with df=7 >1.01) =0.3461 (from student t table)