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A random sample of 49 measurements from a population with population standard deviation ?1 = 3 had a sample mean of x1 = 11. An independent random sample of 64 measurements from a second population with population standard deviation ?2 = 4 had a sample mean of x2 = 13. Test the claim that the population means are different. Use level of significance 0.01.

A random sample of 49 measurements from a population with population standard deviation ?1 = 3 had a sample mean of x1 = 11. An independent random sample of 64 measurements from a second population with population standard deviation ?2 = 4 had a sample mean of x2 = 13. Test the claim that the population means are different. Use level of significance 0.01.

MATLAB: An Introduction with Applications
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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A random sample of 49 measurements from a population with population standard deviation ?1 = 3 had a sample mean of x1 = 11. An independent random sample of 64 measurements from a second population with population standard deviation ?2 = 4 had a sample mean of x2 = 13. Test the claim that the population means are different. Use level of significance 0.01.

A random sample of 49 measurements from a population with population standard deviation ₁-3 had a sample mean of x₁ = 11. An independent random sample of 64 measurements from a second population with population standard deviation ₂ = 4 had a sample mean of x₂ = 13. 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. O The student's t. We assume that both population distributions are approximately normal with known standard deviations. O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The standard normal distribution. Samples are independent, the population standard deviations are known, and the sample sizes are sufficiently large. (b) State the hypotheses. O Ho: H₂H₂i H₁ H₂> H₂ O Ho: H₁ H₂i H₁ H₂ <H₂ о но на = Hzi H1 H1 * H2 о но на * Hzi Hi: H1 H2 (c) Compute x₁-x₂. x₁ - x₂ = Compute the corresponding sample distribution value. (Test the difference #₁ - M₂. 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. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (f) Interpret the results. O Fail to reject the null hypothesis, there is sufficient evidence that there is a difference between the population means. O Reject the null hypothesis, there is insufficient evidence that there is a difference between the population means. O Reject the null hypothesis, there is sufficient evidence that there is a difference between the population means. O Fail to reject the null hypothesis, there is insufficient evidence that there is a difference between the population means. (9) Find a 99% confidence interval for μ₁ - #₂. (Round your answers to two decimal places.) lower limit upper limit Explain the meaning of the confidence interval in the context of the problem. O At the 99% level of confidence, it appears that the difference between population means is between the lower limit and the upper limit. O At the 99% level of confidence, it appears that the difference between population means is equal to the upper limit. O At the 99% level of confidence, it appears that the difference between population means O At the 99% level of confidence, it appears that the difference between population means above the upper limit. below the lower limit.
Transcribed Image Text:A random sample of 49 measurements from a population with population standard deviation ₁-3 had a sample mean of x₁ = 11. An independent random sample of 64 measurements from a second population with population standard deviation ₂ = 4 had a sample mean of x₂ = 13. 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. O The student's t. We assume that both population distributions are approximately normal with known standard deviations. O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The standard normal distribution. Samples are independent, the population standard deviations are known, and the sample sizes are sufficiently large. (b) State the hypotheses. O Ho: H₂H₂i H₁ H₂> H₂ O Ho: H₁ H₂i H₁ H₂ <H₂ о но на = Hzi H1 H1 * H2 о но на * Hzi Hi: H1 H2 (c) Compute x₁-x₂. x₁ - x₂ = Compute the corresponding sample distribution value. (Test the difference #₁ - M₂. 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. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (f) Interpret the results. O Fail to reject the null hypothesis, there is sufficient evidence that there is a difference between the population means. O Reject the null hypothesis, there is insufficient evidence that there is a difference between the population means. O Reject the null hypothesis, there is sufficient evidence that there is a difference between the population means. O Fail to reject the null hypothesis, there is insufficient evidence that there is a difference between the population means. (9) Find a 99% confidence interval for μ₁ - #₂. (Round your answers to two decimal places.) lower limit upper limit Explain the meaning of the confidence interval in the context of the problem. O At the 99% level of confidence, it appears that the difference between population means is between the lower limit and the upper limit. O At the 99% level of confidence, it appears that the difference between population means is equal to the upper limit. O At the 99% level of confidence, it appears that the difference between population means O At the 99% level of confidence, it appears that the difference between population means above the upper limit. below the lower limit.
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