MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Statistical Analysis of Arsenic Levels in Ground Water **Problem Statement:** Arsenic naturally occurs in some groundwater sources. According to the *Union Carbide Technical Report (K/UR-1)*, a mean arsenic level of \( \mu = 8.0 \) parts per billion (ppb) is considered safe for agricultural use. A well in Texas, regularly used to water cotton crops, is being tested for arsenic. A random sample of 37 tests shows a sample mean of \( \bar{x} = 7.2 \) ppb, with a standard deviation \( s = 1.9 \) ppb. #### Objective: To determine if the mean level of arsenic in this well is less than 8 ppb using a significance level of \( \alpha = 0.01 \). ### Hypothesis Testing **a) Level of Significance:** - The significance level is \( \alpha = 0.01 \). **Null and Alternative Hypotheses:** - Null Hypothesis (\( H_0 \)): \( \mu = 8 \) - Alternative Hypothesis (\( H_a \)): \( \mu < 8 \) **b) Sampling Distribution:** - Determine whether to use the normal or t-distribution and compute the appropriate z-score or t-score. **c) P-value:** - Compute or estimate the P-value based on the data collected. **d) Decision Rule:** - Based on the findings from parts (a) through (c), decide whether to reject or fail to reject the null hypothesis. Assess if the data are statistically significant at \( \alpha = 0.01 \). **e) Conclusion:** - Interpret the conclusion in the context of groundwater safety for agricultural purposes. This exercise involves using statistical tools to analyze the safety of groundwater for agricultural use and to make informed decisions based on data.
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Transcribed Image Text:### Statistical Analysis of Arsenic Levels in Ground Water **Problem Statement:** Arsenic naturally occurs in some groundwater sources. According to the *Union Carbide Technical Report (K/UR-1)*, a mean arsenic level of \( \mu = 8.0 \) parts per billion (ppb) is considered safe for agricultural use. A well in Texas, regularly used to water cotton crops, is being tested for arsenic. A random sample of 37 tests shows a sample mean of \( \bar{x} = 7.2 \) ppb, with a standard deviation \( s = 1.9 \) ppb. #### Objective: To determine if the mean level of arsenic in this well is less than 8 ppb using a significance level of \( \alpha = 0.01 \). ### Hypothesis Testing **a) Level of Significance:** - The significance level is \( \alpha = 0.01 \). **Null and Alternative Hypotheses:** - Null Hypothesis (\( H_0 \)): \( \mu = 8 \) - Alternative Hypothesis (\( H_a \)): \( \mu < 8 \) **b) Sampling Distribution:** - Determine whether to use the normal or t-distribution and compute the appropriate z-score or t-score. **c) P-value:** - Compute or estimate the P-value based on the data collected. **d) Decision Rule:** - Based on the findings from parts (a) through (c), decide whether to reject or fail to reject the null hypothesis. Assess if the data are statistically significant at \( \alpha = 0.01 \). **e) Conclusion:** - Interpret the conclusion in the context of groundwater safety for agricultural purposes. This exercise involves using statistical tools to analyze the safety of groundwater for agricultural use and to make informed decisions based on data.
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