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The General Social Survey is an annual survey given to a random selection of about 1500 adults in the United States. Among the many questions asked are "What is the highest level of education you've completed?" and "If you're employed full-time, how many hours do you spend working at your job during a typical week?" In a recent year, 1116 respondents answered both questions. The summary statistics are given in the chart below. (The sample data consist of the times, in hours per week, that were given by the respondents.) Sample Sample Sample Groups size mean variance Less than 281 41.6 115.8 h.s. High school 260 43.3 96.3 Bachelor's 294 42.5 100.5 Graduate 281 44.2 108.2 Send data to Excel Based on these summary statistics, we perform a one-way, independent-samples ANOVA test to determine if there is a difference in the mean hours worked in a typical week among the four populations of workers. (a) The results of this ANOVA are given in the incomplete ANOVA table below. Complete the table. (In the table, round your answers for the mean squares and the F statistic to at least two decimal places each.) Source of Degrees of Sum of variation freedom X G squares Mean square F statistic Between 1038.42 0 0 groups Error (within groups) 0 117,108.20 0 Total 0 118,146.62 (b) What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places. □ X G (c) From the survey data, can we conclude that at least one of the populations differs significantly from the others in mean hours worked in a typical week? Use the 0.10 level of significance. Yes No 5

The General Social Survey is an annual survey given to a random selection of about 1500 adults in the United States. Among the many questions asked are "What is the highest level of education you've completed?" and "If you're employed full-time, how many hours do you spend working at your job during a typical week?" In a recent year, 1116 respondents answered both questions. The summary statistics are given in the chart below. (The sample data consist of the times, in hours per week, that were given by the respondents.) Sample Sample Sample Groups size mean variance Less than 281 41.6 115.8 h.s. High school 260 43.3 96.3 Bachelor's 294 42.5 100.5 Graduate 281 44.2 108.2 Send data to Excel Based on these summary statistics, we perform a one-way, independent-samples ANOVA test to determine if there is a difference in the mean hours worked in a typical week among the four populations of workers. (a) The results of this ANOVA are given in the incomplete ANOVA table below. Complete the table. (In the table, round your answers for the mean squares and the F statistic to at least two decimal places each.) Source of Degrees of Sum of variation freedom X G squares Mean square F statistic Between 1038.42 0 0 groups Error (within groups) 0 117,108.20 0 Total 0 118,146.62 (b) What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places. □ X G (c) From the survey data, can we conclude that at least one of the populations differs significantly from the others in mean hours worked in a typical week? Use the 0.10 level of significance. Yes No 5

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
Section10.6: Summarizing Categorical Data
Problem 4BGP
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The General Social Survey is an annual survey given to a random selection of about 1500 adults in the United States. Among the many questions asked are "What is the highest level of education you've completed?" and "If you're employed full-time, how many hours do you spend working at your job during a typical week?" In a recent year, 1116 respondents answered both questions. The summary statistics are given in the chart below. (The sample data consist of the times, in hours per week, that were given by the respondents.) Sample Sample Sample Groups size mean variance Less than 281 41.6 115.8 h.s. High school 260 43.3 96.3 Bachelor's 294 42.5 100.5 Graduate 281 44.2 108.2 Send data to Excel Based on these summary statistics, we perform a one-way, independent-samples ANOVA test to determine if there is a difference in the mean hours worked in a typical week among the four populations of workers. (a) The results of this ANOVA are given in the incomplete ANOVA table below. Complete the table. (In the table, round your answers for the mean squares and the F statistic to at least two decimal places each.) Source of Degrees of Sum of variation freedom X G squares Mean square F statistic Between 1038.42 0 0 groups Error (within groups) 0 117,108.20 0 Total 0 118,146.62 (b) What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places. □ X G (c) From the survey data, can we conclude that at least one of the populations differs significantly from the others in mean hours worked in a typical week? Use the 0.10 level of significance. Yes No 5
Transcribed Image Text:The General Social Survey is an annual survey given to a random selection of about 1500 adults in the United States. Among the many questions asked are "What is the highest level of education you've completed?" and "If you're employed full-time, how many hours do you spend working at your job during a typical week?" In a recent year, 1116 respondents answered both questions. The summary statistics are given in the chart below. (The sample data consist of the times, in hours per week, that were given by the respondents.) Sample Sample Sample Groups size mean variance Less than 281 41.6 115.8 h.s. High school 260 43.3 96.3 Bachelor's 294 42.5 100.5 Graduate 281 44.2 108.2 Send data to Excel Based on these summary statistics, we perform a one-way, independent-samples ANOVA test to determine if there is a difference in the mean hours worked in a typical week among the four populations of workers. (a) The results of this ANOVA are given in the incomplete ANOVA table below. Complete the table. (In the table, round your answers for the mean squares and the F statistic to at least two decimal places each.) Source of Degrees of Sum of variation freedom X G squares Mean square F statistic Between 1038.42 0 0 groups Error (within groups) 0 117,108.20 0 Total 0 118,146.62 (b) What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places. □ X G (c) From the survey data, can we conclude that at least one of the populations differs significantly from the others in mean hours worked in a typical week? Use the 0.10 level of significance. Yes No 5
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