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Unfortunately, arsenic occurs naturally in some ground water. A mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 31 tests gave a sample mean of x = 6.9 ppb arsenic, with s = 2.4 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.01. USE SALT (a) What is the level of significance? State the null and alternate hypotheses. Ho: μ = 8 ppb; H₁: μ > 8 ppb OH: μ = 8 ppb; H₁: μ< 8 ppb Ho: > 8 ppb; H₁: μ = 8 ppb Ho: μ< 8 ppb; H₁: μ = 8 ppb Ho: μ = 8 ppb; H₁: μ = 8 ppb

Unfortunately, arsenic occurs naturally in some ground water. A mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 31 tests gave a sample mean of x = 6.9 ppb arsenic, with s = 2.4 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.01. USE SALT (a) What is the level of significance? State the null and alternate hypotheses. Ho: μ = 8 ppb; H₁: μ > 8 ppb OH: μ = 8 ppb; H₁: μ< 8 ppb Ho: > 8 ppb; H₁: μ = 8 ppb Ho: μ< 8 ppb; H₁: μ = 8 ppb Ho: μ = 8 ppb; H₁: μ = 8 ppb

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Unfortunately, arsenic occurs naturally in some ground water. † A mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 31 tests gave a sample mean of x = 6.9 ppb arsenic, with s = 2.4 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use α = 0.01. USE SALT (a) What is the level of significance? State the null and alternate hypotheses. Ho: μ = 8 ppb; H₁₂: μ > 8 ppb Ho: μ = 8 ppb; H₁: μ< 8 ppb OH: μ> 8 ppb; H₁: μ = 8 ppb Ho: μ< 8 ppb; H₁: μ = 8 ppb Ho: μ = 8 ppb; H₁: μ ‡ 8 ppb (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since the sample size is large and o is known. The standard normal, since the sample size is large and o is known. The Student's t, since the sample size is large and σ is unknown. The standard normal, since the sample size is large and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. P-value > 0.100 0.050 P-value < 0.100 0.010 < P-value < 0.050 0.005 P-value < 0.010 P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. -2 -2 0 0 2 2 4 4 -4 -2 -2 0 0 2 2 4 4 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the x = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the x = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb. O There is insufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb.
Transcribed Image Text:Unfortunately, arsenic occurs naturally in some ground water. † A mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 31 tests gave a sample mean of x = 6.9 ppb arsenic, with s = 2.4 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use α = 0.01. USE SALT (a) What is the level of significance? State the null and alternate hypotheses. Ho: μ = 8 ppb; H₁₂: μ > 8 ppb Ho: μ = 8 ppb; H₁: μ< 8 ppb OH: μ> 8 ppb; H₁: μ = 8 ppb Ho: μ< 8 ppb; H₁: μ = 8 ppb Ho: μ = 8 ppb; H₁: μ ‡ 8 ppb (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since the sample size is large and o is known. The standard normal, since the sample size is large and o is known. The Student's t, since the sample size is large and σ is unknown. The standard normal, since the sample size is large and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value. P-value > 0.100 0.050 P-value < 0.100 0.010 < P-value < 0.050 0.005 P-value < 0.010 P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. -2 -2 0 0 2 2 4 4 -4 -2 -2 0 0 2 2 4 4 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the x = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the x = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb. O There is insufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb.
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