Question 1075300: The well-known psychologist Dr. Elbod has established what he calls his Generalized Anxiety (GA) scale. This is a Correlation and Regression with (3) questions about 90% confidence intervals for equation “hat" y = 8.44 - 0.33x .
The well-known psychologist Dr. Elbod has established what he calls his Generalized Anxiety (GA) scale. The GA scale, which is a scale from 0 to 10, measures the "general anxiety" of an individual, with higher GA scores corresponding to more anxiety. (Dr. Elbod's assessment of anxiety is based on a variety of measurements, both physiological and psychological.)
We'd like to make predictions about individuals' sleep behavior based on their GA scores. We've collected bivariate data that give the GA score (denoted by ) and the number of hours of sleep last night (denoted by y) for each of the 12 adults participating in a study. The least-squares regression equation for our data is “hat" y = 8.44 - 0.33x . We have used this equation to predict tonight's sleep time for a woman whose GA score is 6.2 We're now interested in both a prediction interval for her sleep time and a confidence interval for the mean sleep time of individuals with her GA score.
We have computed the following for our data:
mean square error (MSE) 0.607;
1/12 + ((6.2 - x bar)^2) / (Summation 12, i=1 (x sub1 - x bar)^2)) = 0.1017;
where x sub 1, x sub 2, …’ x sub 12 denote the GA scores in the sample, and x bar denotes their mean.,
Based on this information, and assuming that the regression assumptions hold, answer the questions in the table below.
1. What is the 90% prediction for an individual value for sleep time (in hours) when eh GA score is 6.2? (Carry your intermediate computations to at least four decimal places, and round your answer to at least two decimal places.)
ANSWER: Lower Limit ______
Answer Upper Limit _______
2. Choose one response to answer the question below.
a). The confidence interval would be positioned to the left of the predication interval
b). The confidence interval would be positioned to the right of the predication interval
c). The confidence interval would have the same center as, but would be wider than, the ….
d). The confidence interval would be identical to the prediction interval.
e). The confidence interval would have the same center as, but would be narrower than, ….
Consider(but do not actually compute) the 90% interval for the mean sleep time when the GA score is 6.2. How would this confidence interval compare to the prediction interval computed above (assuming that both intervals are computed from the same sample data)?
3. Choose one response to answer the question below.
a). The interval computed from a GA score of 2.8 would be narrower, but have the same
a). The interval computed from a GA score of 2.8 would be wider, but have the same
a). The intervals would be identical
a). The interval computed from a GA score of 2.8 would be wider, and have a different
a). The interval computed from a GA score of 2.8 would be narrower, and have a different
For the GA score values in this sample, 2.8 is more extreme than 6.2 is, that is, 2.8 is farther from the sample mean GA score than 6.2 is. How would the 90% prediction interval fro the mean sleep time when the GA score is 2.8 compare to the 90% prediction interval for the mean sleep time when the GA score is 6.2?
Thank you. I also have another similar question so, I would appreciate understanding how to answer this question. THANKS in advance.
Answer by ikleyn(52803)   (Show Source):
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