Answer to Question #302863 in Statistics and Probability for grey

Question

An inventor has developed a new, energy efficient lawn mower engine. He claims that the engine will run continuously for 5 hours (300 minutes) on a single gallon of regular gasoline. Suppose a simple random sample of 50 engines is tested. The engines run for an average of 295 minutes, with a standard deviation of 20 minutes. Test the hypothesis that the mean run time is 300minutes against the alternative hypothesis that the mean run time is not 300minutes using a 0.05 level of significance

Answer 1

$H_0:\mu=300.$

$H_a:\mu \ne300.$

Test statistic: $t=\frac{\bar x-\mu}{\frac{s}{\sqrt{n}}}=\frac{295-300}{\frac{20}{\sqrt{50}}}=-1.77.$

Degrees of freedom: $df=n-1=50-1=49.$

P-value: $p=2P(T<-1.77)=0.0833.$

Since the p-value is greater than 0.05, fail to reject the null hypothesis.

There is no sufficient evidence that the mean run time is not 300 minutes.