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 45 engines is tested. The engines run for an average of 290 minutes, assume the population standard deviation is 20 minutes. Test the null hypothesis that the mean run time is at least 300 minutes. Use a left sided test. Use a 0.025 level of significance.

a) Find the critical value for this test.

b) Find the test statistic
c) Find the p-value for this test.

d) My conclusion is :

e) Is the test statistically significant?

f) Could I use a symmetric confidence interval to solve this problem and if so what is it?