Question

Is the mean lifetime of a particular car engine at least 300,000 miles? To test this claim, a sample of 27 engines is measured, yielding an average of 295,450 miles and a standard deviation of 4200 miles. Use a significance level of 0.01 to test this hypothesis.

A) IEETS B) NEETS C) IEETR D) NEETR ​E) None of the Above

Answer 1

Let the population mean lifetime of a particular car engine be $\mu$

Here we are to test

Ho :μ2 300000 against H, :μ< 300000

The given data is summarized as

Sample size(n)=27

Sample mean($\bar{x}$)=295450

Sample SD(s)=4200

The test statistic is given by

$t=\frac{\bar{x}-300000}{\frac{s}{\sqrt{n}}}$

$\Rightarrow t=\frac{295450-300000}{\frac{4200}{\sqrt{27}}}=\frac{-4550}{808.2903769}=-5.629165125$

The test statistic follows t distribution with df 26

The p-value is obtained to be lesser than 0.00001

As the p-value is less than 0.01, we reject the null hypothesis at 1% level of significance and hence conclude that the population mean lifetime of a particular car engine is less than 300000

The correct option is option C

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