An inventor has developed a new, energy-efficient lawn mower engine. He claims t

Question

An inventor has developed a new, energy-efficient lawn mower engine. He claims that the engine will run continuously for 300 minutes on a single gallon of regular gasoline. From his stock of engines, the inventor selects a random sample of 100 engines for testing. The engines run for an average of 294 minutes, with a standard deviation of 25 minutes. The null hypothesis is that the mean run time is 300 minutes, and the alternative hypothesis is that the mean run time is NOT 300 minutes. At different levels of significance, what is the result of the hypothesis test? The null hypothesis is rejected at 10% and 5%, but not rejected at 1%. The null hypothesis is rejected at 1% and 5%, but not rejected at 10%. The null hypothesis is rejected at 1%, 5% and 10%. The null hypothesis is rejected at 1%, but not rejected at 5% and 10%. The null hypothesis is rejected at 10%, but not rejected at 5% and 1%. The null hypothesis is not rejected at 1%, 5% and 10%.

Explanation / Answer

Ho= u= 300

Ha= u not= 300

it will be two tail test

the crtitical region for 10 % = z<-1.645 and z>1.645

for 5% , z<-1.96 and z>1.96

for 1%. z<-2.575 and z> 2.575

the z static = (294-300)/(25/sqrt(100))

z static = -2.4

hence as the z static = -2.4<-1.96<-1.645 not rejected for 1%

therefore option A is correct

hence will v=be rejected for 10% and 5% and .

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