Here is a summary of their ANOVA test. Fill in the missing entry of the table (r
ID: 3319224 • Letter: H
Question
Here is a summary of their ANOVA test. Fill in the missing entry of the table (rounded to two decimal places), and then answer the questions.
Source of Variation Degrees of Freedom Sum of Squares Mean Square, F Statistic
Between Groups 2 102.87 51.44 ?
Error Within Groups 27 229.5 8.5
Total 29 332.32
How many groups of adults were studied in the experiment?
For the ANOVA test, it is assumed that the variances of REM sleep time percentages are the same for each population of adults. What is an unbiased estimate of this common population variance based on the sample variances?
What is the p-value corresponding to the Fstatistic for the ANOVA test? Round your answer to at least three decimal places.
Can the researchers conclude, using the 0.05 level of significance, that at least one of the populations of adults differs from the others in mean percentage of sleep time spent in REM?
Yes
No
How many groups of adults were studied in the experiment?
For the ANOVA test, it is assumed that the variances of REM sleep time percentages are the same for each population of adults. What is an unbiased estimate of this common population variance based on the sample variances?
What is the p-value corresponding to the Fstatistic for the ANOVA test? Round your answer to at least three decimal places.
Can the researchers conclude, using the 0.05 level of significance, that at least one of the populations of adults differs from the others in mean percentage of sleep time spent in REM?
Yes
No
Explanation / Answer
How many groups of adults were studied in the experiment?
number of groups = 2 +1 = 3
For the ANOVA test, it is assumed that the variances of REM sleep time percentages are the same for each population of adults. What is an unbiased estimate of this common population variance based on the sample variances?
It woule be the Mean square error calcualted in the ANOVA table. It is an unbiased estimate of this common population variance based on the sample variances.
What is the p-value corresponding to the Fstatistic for the ANOVA test? Round your answer to at least three decimal places.
HereF = MSW/MSE = 51.44/8.5 = 6.052
Here p -value = Pr (F = 6.052; 2; 27) = 0.00674
Can the researchers conclude, using the 0.05 level of significance, that at least one of the populations of adults differs from the others in mean percentage of sleep time spent in REM?
Yes as the p - value is less than the 0.05 level of significance, so we shall reject the null hypothesis and can say at least one of the populations of adults differs from the others in mean percentage of sleep time spent in REM.
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