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Earlier this semester, we learned to use 2-Sample-TTest to compare the population means of two independent populations. One-way ANOVA is more powerful because it could compare the population means of three or more independent populations. However, use of one-way ANOVA also requires the assumption that the populations have the same variance. In this exercise, we will compare and contrast One-way ANOVA and 2-Sample-TTest. With the 2-Sample- TTEST, we will first choose 'No' for the pooled variances option, then re-run the test while choosing 'Yes' for the pooled variances option. Use the following data to complete these tasks. Depending on if you choose to do this by hand or using code, use the data format that suits you best LONG form on top or WIDE form on bottom. Treatment Response One 5.6 One 4.7 One 3.6 3.9 5.2 4.3 4.1 4.8 3.4 2.3 4.4 One One One One One Two Two Two Two Two Two Two Two 5.6 4.7 Treatment Treatment One Two 3.4 2.3 4.4 3.5 3.7 5.8 2.8 4.7 3.6 3.9 5.2 4.3 4.1 4.8 3.5 3.7 5.8 2.8 4.7 1. Use One-way ANOVA to test whether the population means are equal (H₁: M₁ M₂) Test Statistics = (Please show your answer to 3 decimal places.) p-value= p-value= (Please show your answer to 4 decimal places) 2. Use 2-Sample-TTest without 'pooled' variances to test whether the population means are equal ( H₁:₁₂) Test Statistics = (Please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places.) 3. Use 2-Sample TTest with 'pooled' variances to test whether the population means are equal ( H₁: M₁ M₂) Test Statistics = p-value= (Please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places.)

Earlier this semester, we learned to use 2-Sample-TTest to compare the population means of two independent populations. One-way ANOVA is more powerful because it could compare the population means of three or more independent populations. However, use of one-way ANOVA also requires the assumption that the populations have the same variance. In this exercise, we will compare and contrast One-way ANOVA and 2-Sample-TTest. With the 2-Sample- TTEST, we will first choose 'No' for the pooled variances option, then re-run the test while choosing 'Yes' for the pooled variances option. Use the following data to complete these tasks. Depending on if you choose to do this by hand or using code, use the data format that suits you best LONG form on top or WIDE form on bottom. Treatment Response One 5.6 One 4.7 One 3.6 3.9 5.2 4.3 4.1 4.8 3.4 2.3 4.4 One One One One One Two Two Two Two Two Two Two Two 5.6 4.7 Treatment Treatment One Two 3.4 2.3 4.4 3.5 3.7 5.8 2.8 4.7 3.6 3.9 5.2 4.3 4.1 4.8 3.5 3.7 5.8 2.8 4.7 1. Use One-way ANOVA to test whether the population means are equal (H₁: M₁ M₂) Test Statistics = (Please show your answer to 3 decimal places.) p-value= p-value= (Please show your answer to 4 decimal places) 2. Use 2-Sample-TTest without 'pooled' variances to test whether the population means are equal ( H₁:₁₂) Test Statistics = (Please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places.) 3. Use 2-Sample TTest with 'pooled' variances to test whether the population means are equal ( H₁: M₁ M₂) Test Statistics = p-value= (Please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places.)

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
Section10.3: Measures Of Spread
Problem 1GP
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Earlier this semester, we learned to use 2-Sample-TTest to compare the population means of two independent populations. One-way ANOVA is more powerful because it could compare the population means of three or more independent populations. However, use of one-way ANOVA also requires the assumption that the populations have the same variance. In this exercise, we will compare and contrast One-way ANOVA and 2-Sample-TTest. With the 2-Sample- TTEST, we will first choose 'No' for the pooled variances option, then re-run the test while choosing 'Yes' for the pooled variances option. Use the following data to complete these tasks. Depending on if you choose to do this by hand or using code, use the data format that suits you best - LONG form on top or WIDE form on bottom. Treatment One One One One One One One One Two Two Two Two Two Two Two Two Treatment Treatment One Two 5.6 4.7 3.6 3.9 5.2 4.3 4.1 4.8 Response 5.6 4.7 3.6 3.9 5.2 4.3 4.1 4.8 3.4 2.3 4.4 3.5 3.7 5.8 2.8 4.7 p-value= 3.4 2.3 4.4 1. Use One-way ANOVA to test whether the population means are equal (H₁: M₁ M₂) Test Statistics = (Please show your answer to 3 decimal places.) p-value = 3.5 3.7 5.8 2.8 4.7 p-value= 2. Use 2-Sample-TTest without 'pooled' variances to test whether the population means are equal ( H₁:1₁ #1₂) Test Statistics = (Please show your answer to 4 decimal places) (Please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places.) 3. Use 2-Sample TTest with 'pooled' variances to test whether the population means are equal ( H₁: M₁ M₂) Test Statistics = (Please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places.)
Transcribed Image Text:Earlier this semester, we learned to use 2-Sample-TTest to compare the population means of two independent populations. One-way ANOVA is more powerful because it could compare the population means of three or more independent populations. However, use of one-way ANOVA also requires the assumption that the populations have the same variance. In this exercise, we will compare and contrast One-way ANOVA and 2-Sample-TTest. With the 2-Sample- TTEST, we will first choose 'No' for the pooled variances option, then re-run the test while choosing 'Yes' for the pooled variances option. Use the following data to complete these tasks. Depending on if you choose to do this by hand or using code, use the data format that suits you best - LONG form on top or WIDE form on bottom. Treatment One One One One One One One One Two Two Two Two Two Two Two Two Treatment Treatment One Two 5.6 4.7 3.6 3.9 5.2 4.3 4.1 4.8 Response 5.6 4.7 3.6 3.9 5.2 4.3 4.1 4.8 3.4 2.3 4.4 3.5 3.7 5.8 2.8 4.7 p-value= 3.4 2.3 4.4 1. Use One-way ANOVA to test whether the population means are equal (H₁: M₁ M₂) Test Statistics = (Please show your answer to 3 decimal places.) p-value = 3.5 3.7 5.8 2.8 4.7 p-value= 2. Use 2-Sample-TTest without 'pooled' variances to test whether the population means are equal ( H₁:1₁ #1₂) Test Statistics = (Please show your answer to 4 decimal places) (Please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places.) 3. Use 2-Sample TTest with 'pooled' variances to test whether the population means are equal ( H₁: M₁ M₂) Test Statistics = (Please show your answer to 3 decimal places.) (Please show your answer to 4 decimal places.)
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