# Question: An industrial plant claims to discharge no more than 1000

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.

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.

**View Solution:**## Answer to relevant Questions

A disadvantage of the experimental design in Example 8 on weight change in anorexic girls is that girls could change weight merely from participating in a study. In fact, girls were randomly assigned to receive a therapy or ...Example 8 described a study about various therapies for teenage girls suffering from anorexia. For each of 17 girls who received the family therapy, the changes in weight were 11, 11, 6, 9, 14, -3, 0, 7, 22, -5, -4, 13, 13, ...Refer to the previous exercise. When we test H0: μ = 0 against Ha: μ > 0, we get a P-value of 0.02. a. What would the decision be for a significance level of 0.05? Interpret in context. b. If the decision in part a is in ...A study considers if the mean score on a college entrance exam for students in 2010 is any different from the mean score of 500 for students who took the same exam in 1985. Let μ represent the mean score for all students ...In Example 13 for testing H0: p = 1/3 (astrologers randomly guessing) with n = 116 when actually p = 0.50, suppose we used Ha: p ≠ 1/3. Then show that: a. A Type II error occurs if 0.248 < p̂ < 0.419. b. The probability ...Post your question