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The following data represent soil water content (percentage of water by volume) for independent random samples of soil taken from two experimental fields growing bell peppers. Soil water content from field 1: X₁; n = 72 15.3 11.3 10.2 10.8 16.6 8.3 9.1 12.3 9.1 14.3 9.5 9.6 11.3 14.0 11.3 10.7 16.1 10.2 15.2 8.9 15.6 11.2 13.8 9.0 8.4 9.6 11.4 8.4 8.0 14.1 11.5 13.1 14.7 12.5 10.2 11.8 8.2 12.0 13.9 11.6 16.0 10.9 13.2 13.8 14.6 10.2 11.0 12.7 10.3 10.8 11.0 12.6 10.8 9.6 11.5 10.6 11.7 10.1 9.7 9.7 11.2 9.8 10.3 11.9 9.7 11.3 10.4 12.0 11.0 10.7 8.9 11.2 Soil water content from field II: x; m₂ = 80 12.1 10.3 13.6 8.1 13.5 7.8 11.8 7.7 8.1 9.2 14.1 8.9 13.9 7.5 12.6 7.3 14.9 12.2 7.6 8.9 13.9 8.4 13.4 7.1 12.4 7.6 9.9 26.0 7.3 7.4 14.3 8.4 13.2 7.3 11.3 7.5 9.7 12.3 6.9 7.6 13.8 7.5 13.3 8.0 11.3 6.8 7.4 11.7 11.8 7.7 12.6 7.7 13.2 13.9 10.4 12.9 7.6 10.7 10.7 10.9 12.5 11.3 10.7 13.2 8.9 12.9 7.7 9.7 9.7 11.4 11.9 13.4 9.2 13.4 8.8 11.9 7.1 8.6 14.0 14.1 LUSE SALT (a) Use a calculator with mean and standard deviation keys to calculate x₁, S1, x2, and sz. (Round your answers to four decimal places.) X1 = S₁ = X₂ = S₂ = (b) Let u be the population mean for x and let z be the population mean for x. Find a 95% confidence interval for μ1-2. (Round your answers to two decimal places.) lower limit

The following data represent soil water content (percentage of water by volume) for independent random samples of soil taken from two experimental fields growing bell peppers. Soil water content from field 1: X₁; n = 72 15.3 11.3 10.2 10.8 16.6 8.3 9.1 12.3 9.1 14.3 9.5 9.6 11.3 14.0 11.3 10.7 16.1 10.2 15.2 8.9 15.6 11.2 13.8 9.0 8.4 9.6 11.4 8.4 8.0 14.1 11.5 13.1 14.7 12.5 10.2 11.8 8.2 12.0 13.9 11.6 16.0 10.9 13.2 13.8 14.6 10.2 11.0 12.7 10.3 10.8 11.0 12.6 10.8 9.6 11.5 10.6 11.7 10.1 9.7 9.7 11.2 9.8 10.3 11.9 9.7 11.3 10.4 12.0 11.0 10.7 8.9 11.2 Soil water content from field II: x; m₂ = 80 12.1 10.3 13.6 8.1 13.5 7.8 11.8 7.7 8.1 9.2 14.1 8.9 13.9 7.5 12.6 7.3 14.9 12.2 7.6 8.9 13.9 8.4 13.4 7.1 12.4 7.6 9.9 26.0 7.3 7.4 14.3 8.4 13.2 7.3 11.3 7.5 9.7 12.3 6.9 7.6 13.8 7.5 13.3 8.0 11.3 6.8 7.4 11.7 11.8 7.7 12.6 7.7 13.2 13.9 10.4 12.9 7.6 10.7 10.7 10.9 12.5 11.3 10.7 13.2 8.9 12.9 7.7 9.7 9.7 11.4 11.9 13.4 9.2 13.4 8.8 11.9 7.1 8.6 14.0 14.1 LUSE SALT (a) Use a calculator with mean and standard deviation keys to calculate x₁, S1, x2, and sz. (Round your answers to four decimal places.) X1 = S₁ = X₂ = S₂ = (b) Let u be the population mean for x and let z be the population mean for x. Find a 95% confidence interval for μ1-2. (Round your answers to two decimal places.) lower limit

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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13 The following data represent soil water content (percentage of water by volume) for independent random samples of soil taken from two experimental fields growing bell peppers. Soil water content from field 1: X₁; m = 72 15.3 11.3 10.2 10.8 16.6 8.3 9.1 12.3 9.1 14.3 10.7 16.1 10.2 15.2 8.9 9.5 9.6 11.3 14.0 11.3 15.6 11.2 13.8 9.0 8.4 8.2 12.0 13.9 11.6 16.0 9.6 11.4 8.4 8.0 14.1 10.9 13.2 13.8 14.6 10.2 11.5 13.1 14.7 12.5 10.2 11.8 11.0 12.7 10.3 10.8 11.0 12.6 10.8 9.6 11.5 10.6 11.7 10.1 9.7 9.7 11.2 9.8 10.3 11.9 9.7 11.3 10.4 12.0 11.0 10.7 8.9 11.2 Soil water content from field II: xz; m2 = 80 12.1 10.3 13.6 8.1 13.5 7.8 11.8 7.7 8.1 9.2 14.1 8.9 13.9 7.5 12.6 7.3 14.9 12.2 7.6 8.9 7.1 12.4 7.6 9.9 26.0 7.3 7.4 13.9 8.4 13.4 14.3 8.4 13.2 13.8 7.5 13.3 8.0 11.3 7.3 11.3 7.5 9.7 12.3 6.9 7.6 6.8 7.4 11.7 11.8 7.7 12.6 7.7 13.2 13.9 10.4 12.9 7.6 10.7 10.7 10.9 12.5 11.3 10.7 13.2 8.9 12.9 7.7 9.7 9.7 11.4 11.9 13.4 9.2 13.4 8.8 11.9 7.1 8.6 14.0 14.1 (a) Use a calculator with mean and standard deviation keys to calculate x₁, S₁, x2, and sz. (Round your answers to four decimal places.) X1 = S₁ = X₂ = USE SALT S₂ = 1 (b) Let u be the population mean for x, and let 2 be the population mean for x₂. Find a 95% confidence interval for μ1-μ 2. (Round your answers to two decimal places.) lower limit upper limit
Transcribed Image Text:13 The following data represent soil water content (percentage of water by volume) for independent random samples of soil taken from two experimental fields growing bell peppers. Soil water content from field 1: X₁; m = 72 15.3 11.3 10.2 10.8 16.6 8.3 9.1 12.3 9.1 14.3 10.7 16.1 10.2 15.2 8.9 9.5 9.6 11.3 14.0 11.3 15.6 11.2 13.8 9.0 8.4 8.2 12.0 13.9 11.6 16.0 9.6 11.4 8.4 8.0 14.1 10.9 13.2 13.8 14.6 10.2 11.5 13.1 14.7 12.5 10.2 11.8 11.0 12.7 10.3 10.8 11.0 12.6 10.8 9.6 11.5 10.6 11.7 10.1 9.7 9.7 11.2 9.8 10.3 11.9 9.7 11.3 10.4 12.0 11.0 10.7 8.9 11.2 Soil water content from field II: xz; m2 = 80 12.1 10.3 13.6 8.1 13.5 7.8 11.8 7.7 8.1 9.2 14.1 8.9 13.9 7.5 12.6 7.3 14.9 12.2 7.6 8.9 7.1 12.4 7.6 9.9 26.0 7.3 7.4 13.9 8.4 13.4 14.3 8.4 13.2 13.8 7.5 13.3 8.0 11.3 7.3 11.3 7.5 9.7 12.3 6.9 7.6 6.8 7.4 11.7 11.8 7.7 12.6 7.7 13.2 13.9 10.4 12.9 7.6 10.7 10.7 10.9 12.5 11.3 10.7 13.2 8.9 12.9 7.7 9.7 9.7 11.4 11.9 13.4 9.2 13.4 8.8 11.9 7.1 8.6 14.0 14.1 (a) Use a calculator with mean and standard deviation keys to calculate x₁, S₁, x2, and sz. (Round your answers to four decimal places.) X1 = S₁ = X₂ = USE SALT S₂ = 1 (b) Let u be the population mean for x, and let 2 be the population mean for x₂. Find a 95% confidence interval for μ1-μ 2. (Round your answers to two decimal places.) lower limit upper limit
(e) Use x = 0.01 to test the claim that the population mean soil water content of the first field is higher than that of the second. (i) What is the level of significance? State the null and alternate hypotheses. Ho: μ γ # μ z M: μη=μή 1 μl 2; H₁: μ 1 # μl 2 H₂:μ ₁ = μ₂; H₁ H1> H ₂ Ho:μι = με Ημι<με (ii) 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 Student's t. 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 standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. (iii) Find (or estimate) the P-value. P-value > 0.250 0.125 < P-value < 0.250 0.005 < P-value < 0.025 P-value < 0.005 What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ 1-μ2. Do not use rounded values. Round your answer to three decimal places.) H₂:44 1 = 0.050 < P-value < 0.125 0.025 < P-value < 0.050 Sketch the sampling distribution and show the area corresponding to the P-value. L
Transcribed Image Text:(e) Use x = 0.01 to test the claim that the population mean soil water content of the first field is higher than that of the second. (i) What is the level of significance? State the null and alternate hypotheses. Ho: μ γ # μ z M: μη=μή 1 μl 2; H₁: μ 1 # μl 2 H₂:μ ₁ = μ₂; H₁ H1> H ₂ Ho:μι = με Ημι<με (ii) 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 Student's t. 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 standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. (iii) Find (or estimate) the P-value. P-value > 0.250 0.125 < P-value < 0.250 0.005 < P-value < 0.025 P-value < 0.005 What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ 1-μ2. Do not use rounded values. Round your answer to three decimal places.) H₂:44 1 = 0.050 < P-value < 0.125 0.025 < P-value < 0.050 Sketch the sampling distribution and show the area corresponding to the P-value. L
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