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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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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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