Unfortunately, arsenic occurs naturally in some ground watert. A mean arsenic level of u = 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 41 tests gave a sample mean of x = 6.9 ppb arsenic, with s = 2.8 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. O Họ: H < 8 ppb; H1: µ = 8 ppb O Họ: H = 8 ppb; H1: H + 8 ppb O Ho: µ = 8 ppb; H1: µ < 8 ppb O Ho: H = 8 ppb; H1: u > 8 ppb O Họ: H > 8 ppb; H1: u = 8 ppb (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large and o is unknown. O The standard normal, since the sample size is large and o is known. O The Student's t, since the sample size is large and o is known. O 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) Find the P-value. (Round your answer to four decimal places.)
Unfortunately, arsenic occurs naturally in some ground watert. A mean arsenic level of u = 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 41 tests gave a sample mean of x = 6.9 ppb arsenic, with s = 2.8 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. O Họ: H < 8 ppb; H1: µ = 8 ppb O Họ: H = 8 ppb; H1: H + 8 ppb O Ho: µ = 8 ppb; H1: µ < 8 ppb O Ho: H = 8 ppb; H1: u > 8 ppb O Họ: H > 8 ppb; H1: u = 8 ppb (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since the sample size is large and o is unknown. O The standard normal, since the sample size is large and o is known. O The Student's t, since the sample size is large and o is known. O 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) Find the P-value. (Round your answer to four decimal places.)
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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![**Understanding Arsenic Levels in Groundwater**
Unfortunately, arsenic occurs naturally in some groundwater. A mean arsenic level of \( \mu = 8.0 \) 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 41 tests gave a sample mean of \( \bar{x} = 6.9 \) ppb arsenic, with \( s = 2.8 \) ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use \( \alpha = 0.05 \).
**(a) What is the level of significance?**
[Input box for level of significance]
**State the null and alternate hypotheses:**
- \( H_0: \mu < 8 \text{ ppb}; H_1: \mu = 8 \text{ ppb} \)
- \( H_0: \mu = 8 \text{ ppb}; H_1: \mu \neq 8 \text{ ppb} \)
- \( H_0: \mu = 8 \text{ ppb}; H_1: \mu < 8 \text{ ppb} \)
- \( H_0: \mu = 8 \text{ ppb}; H_1: \mu > 8 \text{ ppb} \)
- \( H_0: \mu > 8 \text{ ppb}; H_1: \mu = 8 \text{ ppb} \)
**(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 \( \sigma \) is unknown.
- The standard normal, since the sample size is large and \( \sigma \) is known.
- The Student's \( t \), since the sample size is large and \( \sigma \) is known.
- The standard normal, since the sample size is large and \( \sigma \) is unknown.
**What is the value of the sample test statistic? (Round your answer to three decimal places.)**
[Input box for sample test statistic]
**(c) Find the \( P \)-value. (Round your](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F263d6acc-03b4-45b5-8ce2-d676aa9ac999%2F3dac30ea-ac8c-4ff4-a30d-ce1816f3029c%2Fyywjjih_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Arsenic Levels in Groundwater**
Unfortunately, arsenic occurs naturally in some groundwater. A mean arsenic level of \( \mu = 8.0 \) 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 41 tests gave a sample mean of \( \bar{x} = 6.9 \) ppb arsenic, with \( s = 2.8 \) ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use \( \alpha = 0.05 \).
**(a) What is the level of significance?**
[Input box for level of significance]
**State the null and alternate hypotheses:**
- \( H_0: \mu < 8 \text{ ppb}; H_1: \mu = 8 \text{ ppb} \)
- \( H_0: \mu = 8 \text{ ppb}; H_1: \mu \neq 8 \text{ ppb} \)
- \( H_0: \mu = 8 \text{ ppb}; H_1: \mu < 8 \text{ ppb} \)
- \( H_0: \mu = 8 \text{ ppb}; H_1: \mu > 8 \text{ ppb} \)
- \( H_0: \mu > 8 \text{ ppb}; H_1: \mu = 8 \text{ ppb} \)
**(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 \( \sigma \) is unknown.
- The standard normal, since the sample size is large and \( \sigma \) is known.
- The Student's \( t \), since the sample size is large and \( \sigma \) is known.
- The standard normal, since the sample size is large and \( \sigma \) is unknown.
**What is the value of the sample test statistic? (Round your answer to three decimal places.)**
[Input box for sample test statistic]
**(c) Find the \( P \)-value. (Round your
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