Question

A computer manufacturer estimates that its line of minicomputers has, on average, 7.5 days of downtime per year. To test this claim, a researcher contacts seven companies that own one of these computers and is allowed to access company computer records. It is determined that, for the sample, the average number of downtime days is 4.1, with a sample standard deviation of 1.1 days. Assuming that number of downtime days is normally distributed, test to determine whether these minicomputers actually average 7.5 days of downtime in the entire population. Let α = .01.

Answer 1

We have to test the hypothesis

Our assumption is that population is normal , and as we donot know the varaince of population ,so we will use t test

sample size=7

sample mean ==4.1

sample standard deviation= s=1.1

t statistics is given by

this follows t distribution with n-1 degree of freedom

hence using the values above in formula we get ,

Tabulated value of t at 0.01 level of significance and 6 degree of freedom is 3.70

Since calculated value of |t| is greater than tabulated we reject the null hypothesis and conclude that