Suppose that you suspect nutrient overload in stream water, especially phosphorus. It is generally considered that the upper limit of phosphorus amount in natural water is 0.05 mg/L. You want to test whether the stream has a larger amount of phosphorus than this upper limit. You randomly take a water sample of size 16 from the stream. The mean phosphorus amount in the sample is 0.053 mg/L and the standard deviation is 0.008 mg/L. Perform the hypothesis test using the significance level of 0.05 by completing the following steps. Refer to the examples in the textbook 9.5.

Question 1. Write down the null and alternative hypothesis using words. (10 pts.)

Question 2. Write down the null and alternative hypothesis using symbols. (10 pts.)

Question 3. What is the value of in this hypothesis test? (10 pts.)

Question 4. Determine an appropriate distribution (standard normal distribution or t-distribution) to use. State the reason to support your choice. (10 pts.)

Question 5. Sketch the distribution (by hand or digitally) selected above and shade the area where your null hypothesis is rejected. (10 pts.)

Question 6. Calculate the value of the test statistic. Show your work. (10 pts.)

Question 7. Determine the p-value using an appropriate table or other technology (e.g. calculator). (10 pts.)

Question 8. Compare the p-value and the value of . Then determine whether you should reject or not reject the null hypothesis. (10 pts.)

Question 9. State the conclusion of the hypothesis testing in 10-20 words