Question

9.6

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 5.6, 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 8.7 days of downtime in the entire population. Let α = .01.

Appendix A Statistical Tables

(Round your answer to 2 decimal places.)

The value of the test statistic is enter the value of the test statistic and we choose between reject and fail to reject the null hypothesis                                                          reject the null hypothesisfail to reject the null hypothesis.

Answer 1

Solution:

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 8.7

Ha: 8.7

The test statistics,

t = ( - )/ (s/)

= ( 5.6 - 8.7 ) / ( 1.1 / 7 )

= - 7.456

Critical value of  the significance level is α = 0.01, and the critical value for a two-tailed test is

= 3.707

Since it is observed that |t| = 7.456 > = 3.707, it is then concluded that the null hypothesis is rejected.

P-value = 0.0003

The p-value is p = 0.0003 < 0.01, it is concluded that the null hypothesis is rejected.