An industrial plant claims to discharge no more than 1000 gallons of wastewater per hour, on the average, into a neighboring lake. An environmental action group decides to monitor the plant, in case this limit is being exceeded. Doing so is expensive, and only a small sample is possible. A random sample of four hours is selected over a period of a week. The observations (gallons of wastewater discharged per hour) are 2000, 1000, 3000, 2000.
a. Show that x = 2000, s = 816.5, and standard error = 408.25.
b. To test H0: μ = 1000 vs. Ha: μ > 1000, show that the test statistic equals 2.45.
c. Using Table B or software, show that the P-value is less than 0.05, so there is enough evidence to reject the null hypothesis at the 0.05 significance level.
d. Explain how your one-sided analysis in part b implicitly tests the broader null hypothesis that μ . 1000.