Unfortunately, arsenic occurs naturally in some ground water.† A mean arsenic level of μ = 8.3 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 = 7.3 ppb arsenic, with s = 2.4 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8.3 ppb? Use ? = 0.01. (a) What is the level of significance? State the null hypotheses H0 and the alternate hypothesis H1 . H0 : μ ---Select--- < ≥ ≤ = > ≠ H1 : μ ---Select--- < > ≤ ≥ = ≠ (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and σ is known.The Student's t, since the sample size is large and σ is known. The standard normal, since the sample size is large and σ is unknown. The Student's t, since the sample size is large and σ is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Compute the P-value. (Round your answer to four decimal places.) 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 ?? At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ? = 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 8.3 ppb. There is insufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8.3 ppb.

Unfortunately, arsenic occurs naturally in some ground water.† A mean arsenic level of μ = 8.3 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 = 7.3 ppb arsenic, with s = 2.4 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8.3 ppb? Use ? = 0.01. (a) What is the level of significance? State the null hypotheses H0 and the alternate hypothesis H1 . H0 : μ ---Select--- < ≥ ≤ = > ≠ H1 : μ ---Select--- < > ≤ ≥ = ≠ (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and σ is known.The Student's t, since the sample size is large and σ is known. The standard normal, since the sample size is large and σ is unknown. The Student's t, since the sample size is large and σ is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Compute the P-value. (Round your answer to four decimal places.) 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 ?? At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ? = 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 8.3 ppb. There is insufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8.3 ppb.

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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Question

(a)

What is the level of significance?

State the null hypotheses

H₀

and the alternate hypothesis

H₁

H₀

: μ ---Select--- < ≥ ≤ = > ≠

H₁

: μ ---Select--- < > ≤ ≥ = ≠

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since the sample size is large and σ is known.The Student's t, since the sample size is large and σ is known.

The standard normal, since the sample size is large and σ is unknown.

The Student's t, since the sample size is large and σ is unknown.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

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 ??

At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the ? = 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 8.3 ppb.

There is insufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8.3 ppb.

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