In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 12 modified components resulted in the following times (in hours) between failures. 518 548 561 523 536 522 499 538 557 528 563 530 At the 0.05 significance level, test the claim that for the modified components, the mean time between failures is greater than 520 hours. Assume the data comes from a population that is essentially normal.
| null hypothesis: HO: μ | = | 520 | ||
| Alternate Hypothesis: Ha: μ | > | 520 | ||
| 0.05 level with right tail test and n-1= 11 df, critical t= | 1.796 | |||
| Decision rule :reject Ho if test statistic t>1.796 | ||||
| population mean μ= | 520 | |||
| sample mean 'x̄= | 535.250 | |||
| sample size n= | 12.00 | |||
| std deviation s= | 19.293 | |||
| std error ='sx=s/√n= | 5.5693 | |||
| test stat t ='(x-μ)*√n/sx= | 2.738 | |||
| since test statistic falls in rejection region we reject null hypothesis |
| we have sufficient evidence to conclude that the mean time between failures is greater than 520 hours. |
Get Answers For Free
Most questions answered within 1 hours.