A random sample of n1 = 49 measurements from a population with population standard deviation ?1 = 3 had a sample mean of x1 = 9. An independent random sample of n2 = 64 measurements from a second population with population standard deviation ?2 = 4 had a sample mean of x2 = 11. Test the claim that the population means are different. Use level of significance 0.01.(a) Check Requirements: 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 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.(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(c) Compute x1 − x2.x1 − x2 = Compute the corresponding sample distribution value. (Test the difference ?1 − ?2. Round your answer to two decimal places.)(d) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)(e) Conclude the test.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 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.Fail to reject the null hypothesis, there is insufficient 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. Reject the null hypothesis, there is sufficient 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.

Answered: A random sample of n1 = 49…

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

A random sample of

n₁ = 49

measurements from a population with population standard deviation

?₁ = 3

had a sample mean of

x₁ = 9.

An independent random sample of

n₂ = 64

measurements from a second population with population standard deviation

?₂ = 4

had a sample mean of

x₂ = 11.

Test the claim that the population means are different. Use level of significance 0.01.

(a) Check Requirements: 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 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.

(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 two decimal places.)

(d) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)

(e) Conclude the test.

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 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.

Fail to reject the null hypothesis, there is insufficient 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. Reject the null hypothesis, there is sufficient 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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