An inventor has developed a new, energy-efficient lawn mower engine. The claim i

Question

An inventor has developed a new, energy-efficient lawn mower engine. The claim is that the engine will run continuously for 5 hours (300 minutes) on a single gallon of gasoline. From a stock of 2000 engines, the inventor selects a simple random sample of 50 engines for testing. The engines run for an average of 295 minutes, with a standard deviation of 20 minutes. Using a two-sided test, state the appropriate hypotheses, and decide whether the requirement is satisfied at a significance level of 0.05. Discuss what the sample size would need to be in order for the p-value to be 0.05 (assume that the sample mean and standard deviation remain the same values of 295 and 20 minutes, respectively). Interpolate in tables as needed.

Explanation / Answer

Set Up Hypothesis
Null, H0: U=300
Alternate, H1: U!=300
Test Statistic
Population Mean(U)=300
Sample X(Mean)=295
Standard Deviation(S.D)=20
Number (n)=50
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =295-300/(20/Sqrt(50))
to =-1.768
| to | =1.768
Critical Value
The Value of |t | with n-1 = 49 d.f is 2.01
We got |to| =1.768 & | t | =2.01
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != -1.7678 ) = 0.0833
Hence Value of P0.05 < 0.0833,Here We Do not Reject Ho

Requirement is satisfied at the given LOS

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