Worksheet4

.docx

School

Unity College *

*We aren’t endorsed by this school

Course

201

Subject

Mathematics

Date

Feb 20, 2024

Type

docx

Pages

3

Uploaded by PrivateComputerSparrow38

MATH 201 Statistics for Environmental Professionals ● Worksheet 4 Name Section 1. 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 more 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.) Null: The stream water has a phosphorus amount of 0.05 mg/L or less. Alternative: The stream water has a phosphorus amount greater than 0.05 mg/L. Question 2. Write down the null and alternative hypothesis using symbols. (10 pts.) Null: H0: µ ≤ 0.05mg/L Alternative: Ha: µ > 0.05mg/L Question 3. What is the value of α in this hypothesis test? (10 pts.) 0.05 Question 4. Determine an appropriate distribution (standard normal distribution or t-distribution) to use. State the reason to support your choice. (10 pts.) We should use the t-distribution because the population standard deviation is unknown and the sample size is less than 30. 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.) T = (0.053-0.05)/(0.008/√16) = 2
Question 7. Determine the p-value using an appropriate table or other technology (e.g. calculator). (10 pts.) 0.034 Question 8. Compare the p-value and the value of α. Then determine whether you should reject or not reject the null hypothesis. (10 pts.) The p-value is less than the value of a (0.034 < 0.05), so we reject the null hypothesis. Question 9. State the conclusion of the hypothesis testing in 10-20 words. (10 pts.) We have sufficient evidence to conclude that the stream water has a phosphorus amount greater than 0.05mg/L.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help