MATH201_Worksheet4(submission)

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Unity College *

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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 a more significant 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.) Null Hypothesis (H0): The average amount of phosphorus in the stream water is 0.05 mg/L or less. Alternative Hypothesis (H1): The average amount of phosphorus in the stream water is more significant than 0.05 mg/L. Question 2. Write down the null and alternative hypothesis using symbols. (10 pts.) H0: μ ≤ 0.05 H1: μ > 0.05 Question 3. What is the value of α in this hypothesis test? (10 pts.) Given that I am using a significance level of 0.05, the value of α for this hypothesis test is 0.05 or 5%. This means I am willing to accept a 5% chance of incorrectly rejecting the null hypothesis when it is true. Question 4. Determine an appropriate distribution (standard normal distribution or t-distribution) to use. State the reason to support your choice. (10 pts.) Since the population standard is unknown and the sample size is 16, which is considered small (commonly defined as less than 30), it is more appropriate to use the t-distribution. The t-distribution accounts for the additional uncertainty introduced by estimating the population standard deviation from a small sample. 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.) The p-value is 0.077. 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.) Since the p-value (0.077183) is greater than α (0.05), there is insufficient evidence to reject the null hypothesis at the 0.05 significance level. The results are not statistically significant, and I fail to reject the null hypothesis. Question 9. State the conclusion of the hypothesis testing in 10-20 words.(10 pts.)
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