Worksheet4

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Mathematics

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Feb 20, 2024

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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.

Section 2. The accompanied data is a part of a dataset of measured phosphorus amount (kilograms/hectare/year) by watershed. We want to test whether the mean phosphorus amount exceeds 0.55 kilograms/hectare/year. Calculate and report appropriate test statistics and p-values using the provided Excel spreadsheet. (10 pts.) Watershed TOTAL UPPER DELAWARE 0.3886 EAST BRANCH DELAWARE 0.3176 LACKAWAXEN 0.3651 MIDDLE DELAWARE-MONGAUP -0.3175 MIDDLE DELAWARE-MUSCONET 0.6457 LEHIGH 0.5521 CROSSWICKS-NESHAMINY 0.8097 LOWER DELAWARE 0.7781 SCHUYLKILL 0.7025 BRANDYWINE-CHRISTINA 0.8449 COHANSEY-MAURICE 0.6191 BROADKILL-SMYRNA 1.0916 UPPER SUSQUEHANNA 0.4813 CHENANGO 0.5143 OWEGO-WAPPASENING 0.4794 TIOGA 0.5262 CHEMUNG 0.5495 UPPER SUSQUEHANNA-TUNKHA 0.5312 UPPER SUSQUEHANNA-LACKAW 0.5349 UPPER WEST BRANCH SUSQUEHANNA 0.3469 Test statistic: -0.232 P-value: 0.41

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Worksheet4

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