A car manufacturer, Swanson, claims that the mean lifetime of one of its car engines is greater than 220000 miles, which is the mean lifetime of the engine of a competitor. The mean lifetime for a random sample of 23 of the Swanson engines was with mean of 226450 miles with a standard deviation of 11500 miles. Test the Swanson’s claim using a significance level of 0.01. What is your conclusion?
| null hypothesis: HO: μ | = | 220000 | |||
| Alternate Hypothesis: Ha: μ | > | 220000 | |||
| 0.01 level with right tail test and n-1= 22 df, critical t= | 2.508 | from excel: t.inv(0.99,22) | |||
| Decision rule :reject Ho if test statistic t>2.508 | |||||
| population mean μ= | 220000 | ||||
| sample mean 'x̄= | 226450.00 | ||||
| sample size n= | 23 | ||||
| std deviation s= | 11500.000 | ||||
| std error ='sx=s/√n=11500/√23= | 2397.916 | ||||
| t statistic ='(x̄-μ)/sx=(226450-220000)/2397.916= | 2.690 | ||||
| p value = | 0.0067 | from excel: tdist(2.69,22,1) | |||
| since test statistic falls in rejection region we reject null hypothesis |
| we have sufficient evidence to conclude that mean lifetime of its car engines is greater than 220000 miles |
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