Question

A computer manufacturer estimates that its line of minicomputers has, on average, 8.7 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 5.2, with a sample standard deviation of 1.6 days. Assuming that number of downtime days is normally distributed, test to determine whether these minicomputers actually average 8.7 days of downtime in the entire population. Let α = .01.

Answer 1

We need to use the testing of hypothesis thoery.

Here the population standard deviation is unknown hence the test statistic under null hypothesis will follow t distribution.

H0 : the average days of downtime of computers is 8.7

V/s

H1 : the average days of downtime of computers is not 8.7

Conclusion :

The minicomputers may not average 8.7 days of downtime in the entire population.