Question

Test runs with 6 models of an experimental engine showed that they operated for 24, 28, 21, 23, 32, and 22 minutes on a gallon of a certain kind of fuel.  If the probability of a Type I error is to be at most 0.01, is this evidence against a hypothesis that on the average this kind of engine will operate for at least 29 minutes per gallon with this kind of fuel?  Assume normality. - Perform a hypothesis test.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ >= 29
Alternative Hypothesis, Ha: μ < 29

Rejection Region
This is left tailed test, for α = 0.01 and df = 5
Critical value of t is -3.365.
Hence reject H0 if t < -3.365

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (25 - 29)/(4.1952/sqrt(6))
t = -2.336

P-value Approach
P-value = 0.0334

As P-value >= 0.01, fail to reject null hypothesis.

There is evidence that on the average this kind of engine will operate for at least 29 minutes per gallon with this kind of fuel