Answered: A random sample of 49 measurements from…

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 random sample of 49 measurements from one population had a sample mean of 16, with sample standard deviation 5. An independent random sample of 64 measurements from a second population had a sample mean of 19, with sample standard deviation 6. Test the claim that the population means are different. Use level of significance 0.01.

(a) What distribution does the sample test statistic follow? Explain.

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 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.

(b) State the hypotheses.

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

x₁ − x₂.

x₁ − x₂ =

Compute the corresponding sample distribution value. (Test the difference ?₁ − ?₂. Round your answer to three decimal places.)

(d) Estimate the P-value of the sample test statistic.

P-value > 0.5000.250 < P-value < 0.500 0.100 < P-value < 0.2500.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

(e) Conclude the test.

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.

(f) Interpret the results.

Reject the null hypothesis, there is sufficient evidence that there is a difference between the population means.Reject the null hypothesis, there is insufficient evidence that there is a difference between the population means. Fail to reject the null hypothesis, there is insufficient evidence that there is a difference between the population means.Fail to reject the null hypothesis, there is sufficient evidence that there is a difference between the population means.

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