he 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?" na recent year, 1079 respondents answered both questions. The summary statistics are given in the chart below. (The sample data consist of the times, in ours per week, that were given by the respondents.) Sample Sample Sample size Groups mean variance Less than h.s. High school 258 40.9 101.8 263 41.8 97.5 Bachelor's 270 42.2 94.4 Graduate 288 43.0 98.7 Send data to calculator v Send data to Excel o decide if there are any differences in the mean hours per week worked by these different groups, we can perform a one-way, independent-samples ANOVA est. Such a test uses the following statistic.
he 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?" na recent year, 1079 respondents answered both questions. The summary statistics are given in the chart below. (The sample data consist of the times, in ours per week, that were given by the respondents.) Sample Sample Sample size Groups mean variance Less than h.s. High school 258 40.9 101.8 263 41.8 97.5 Bachelor's 270 42.2 94.4 Graduate 288 43.0 98.7 Send data to calculator v Send data to Excel o decide if there are any differences in the mean hours per week worked by these different groups, we can perform a one-way, independent-samples ANOVA est. Such a test uses the following statistic.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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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, 1079 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.)
| Groups | Sample size | Sample mean | Sample variance |
|----------------|-------------|-------------|-----------------|
| Less than h.s. | 258 | 40.9 | 101.8 |
| High school | 263 | 41.8 | 97.5 |
| Bachelor's | 270 | 42.2 | 94.4 |
| Graduate | 288 | 43.0 | 98.7 |
To decide if there are any differences in the mean hours per week worked by these different groups, we can perform a one-way, independent-samples ANOVA test. Such a test uses the following statistic:
\[ F = \frac{\text{Variation between the samples}}{\text{Variation within the samples}} \]
For the data from the survey, \( F \approx 2.12 \).
**Questions:**
(a) Give the numerator degrees of freedom of this \( F \) statistic.
(b) Give the denominator degrees of freedom of this \( F \) statistic.
(c) From the survey data, can we conclude that at least one of the groups differs significantly from the others in mean hours worked in a typical week? Use the 0.05 level of significance.
Options: Yes / No](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F438f9e3e-5163-4042-928f-6af00166f2ed%2Fd953e5f5-be63-4d5e-b5ca-70014fc1bac5%2F52owl1o_processed.png&w=3840&q=75)
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, 1079 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.)
| Groups | Sample size | Sample mean | Sample variance |
|----------------|-------------|-------------|-----------------|
| Less than h.s. | 258 | 40.9 | 101.8 |
| High school | 263 | 41.8 | 97.5 |
| Bachelor's | 270 | 42.2 | 94.4 |
| Graduate | 288 | 43.0 | 98.7 |
To decide if there are any differences in the mean hours per week worked by these different groups, we can perform a one-way, independent-samples ANOVA test. Such a test uses the following statistic:
\[ F = \frac{\text{Variation between the samples}}{\text{Variation within the samples}} \]
For the data from the survey, \( F \approx 2.12 \).
**Questions:**
(a) Give the numerator degrees of freedom of this \( F \) statistic.
(b) Give the denominator degrees of freedom of this \( F \) statistic.
(c) From the survey data, can we conclude that at least one of the groups differs significantly from the others in mean hours worked in a typical week? Use the 0.05 level of significance.
Options: Yes / No
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