STA 106 Homework 4 Solutions
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STA 106 Homework 4 Solutions
Book Problems
1. (a) The errors look approximately normal - with very few points a large distance from the line, and the histogram approximately symmetric.
(b) There do not appear to be any outliers, by all three graphs. All points are close together, and none show as unusual.
(c) The variance of each group do appear to be equal, although they are off set.
(d) No. There are so few points in each group that removing more is not recommended.
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2. (a) |
We fail to reject the null and conclude there is evidence to suggest the errors are normally distributed. |
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(b) |
We fail to reject the null and conclude there is evidence to suggest that the group variances are equal. |
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(c) |
No. The tests for the assumptions of ANOVA are met, so that there is no need to transform the data. |
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(d) |
Since we concluded our data followed the assumptions of ANOVA, yes we believe they are reliable. |
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3. (a) |
No. There appears to be very unequal variances, and outliers which cause non-normality. |
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(b) |
H0 : The data (errors) are normally distributed vs. HA : The data (errors) are not normally distributed. |
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(c) |
H0 : The groups have equal variance vs. HA : At least one of the groups does not have equal variance. |
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(d) |
No. Since it appears our assumptions of ANOVA are violated, all results based off of those assumptions are likely to have serious errors. |
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4. (a) |
If in reality the data (errors) were normally distributed, we would observe our data or more extreme with probability 0.0734. |
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(b) |
If in reality the groups had equal variance, we would observe our sample data or more extreme with probability 0.0000304. |
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2022-05-25