The highway department is testing two types of reflecting paint for concrete bridge end pillars. The two kinds of paint are alike in every respect except that one is orange and the other is yellow. The orange paint is applied to 12 bridges, and the yellow paint is applied to 12 bridges. After a period of 1 year, reflectometer readings were made on all these bridge end pillars. (A higher reading means better visibility.) For the orange paint, the mean reflectometer reading was x1 = 9.4, with standard deviation s1 = 2.4. For the yellow paint the mean was x2 = 6.9, with standard deviation s2 = 2.2. Based on these data, can we conclude that the yellow paint has less visibility after 1 year? Use a 1% level of significance. What are we testing in this problem? single meandifference of proportions single proportiondifference of meanspaired difference (a) What is the level of significance? State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 < ?2H0: ?1 = ?2; H1: ?1 ≠ ?2 H0: ?1 = ?2; H1: ?1 > ?2H0: ?1 > ?2; H1: ?1 = ?2 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The Student's t. We assume that both population distributions are approximately normal with known standard deviations.The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference ?1 − ?2. Round your answer to three decimal places.) (c) Find (or estimate) the P-value. P-value > 0.2500.125 < P-value < 0.250 0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. (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 ?? At the ? = 0.01 level, we 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. 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. (e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.01 level that the yellow paint has less visibility after 1 year.There is insufficient evidence at the 0.01 level that the yellow paint has less visibility after 1 year.

The highway department is testing two types of reflecting paint for concrete bridge end pillars. The two kinds of paint are alike in every respect except that one is orange and the other is yellow. The orange paint is applied to 12 bridges, and the yellow paint is applied to 12 bridges. After a period of 1 year, reflectometer readings were made on all these bridge end pillars. (A higher reading means better visibility.) For the orange paint, the mean reflectometer reading was x1 = 9.4, with standard deviation s1 = 2.4. For the yellow paint the mean was x2 = 6.9, with standard deviation s2 = 2.2. Based on these data, can we conclude that the yellow paint has less visibility after 1 year? Use a 1% level of significance. What are we testing in this problem? single meandifference of proportions single proportiondifference of meanspaired difference (a) What is the level of significance? State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 < ?2H0: ?1 = ?2; H1: ?1 ≠ ?2 H0: ?1 = ?2; H1: ?1 > ?2H0: ?1 > ?2; H1: ?1 = ?2 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The Student's t. We assume that both population distributions are approximately normal with known standard deviations.The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference ?1 − ?2. Round your answer to three decimal places.) (c) Find (or estimate) the P-value. P-value > 0.2500.125 < P-value < 0.250 0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. (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 ?? At the ? = 0.01 level, we 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. 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. (e) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.01 level that the yellow paint has less visibility after 1 year.There is insufficient evidence at the 0.01 level that the yellow paint has less visibility after 1 year.

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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Related questions

Question

What are we testing in this problem?

single meandifference of proportions single proportiondifference of meanspaired difference

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: ?₁ = ?₂; H₁: ?₁ < ?₂H₀: ?₁ = ?₂; H₁: ?₁ ≠ ?₂ H₀: ?₁ = ?₂; H₁: ?₁ > ?₂H₀: ?₁ > ?₂; H₁: ?₁ = ?₂

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The Student's t. We assume that both population distributions are approximately normal with known standard deviations.The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.

What is the value of the sample test statistic? (Test the difference ?₁ − ?₂. Round your answer to three decimal places.)

(c) Find (or estimate) the P-value.

P-value > 0.2500.125 < P-value < 0.250 0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005

Sketch the sampling distribution and show the area corresponding to the P-value.

(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 ??

At the ? = 0.01 level, we 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. 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.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level that the yellow paint has less visibility after 1 year.There is insufficient evidence at the 0.01 level that the yellow paint has less visibility after 1 year.

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