4.docx
*Round all answers to two decimal places, unless otherwise noted.
We would like to determine how the time a student spends studying for an exam affects his or her score. Study times (in hours) and exam scores (in %) are shown in the table below for a sample of eight students:
|
Study Time
|
11
|
23
|
5
|
14
|
3
|
17
|
28
|
8
|
|
Score
|
50
|
94
|
41
|
82
|
62
|
73
|
85
|
64
|
From these data, we calculate ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%40OVERBAR%7Bx%7D%3D13.625]()
, ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%40OVERBAR%7By%7D%3D68.875]()
, sx = 8.72, sy = 18.07, r = 0.795, ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%40SUM%7B%7D(x%40SUB%7Bi%7D-%40OVERBAR%7Bx%7D)%40SUP%7B2%7D%3D531.87]()
and ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%40SUM%7B%7D(y%40SUB%7Bi%7D-%40HAT%7By%7D)%40SUP%7B2%7D%3D840.03]()
.
(a) The equation of the least squares regression line is + x.
(b) What percentage of the variation in Exam Score is accounted for by its regression on Study Time? %
(c) What is the predicted Exam Score for a student who studies 10 hours?
(d) What is the value of the residual for the student in the sample who studied for 17 hours?
(e) The estimate of the parameter ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%26sigma%3B]()
in the regression model is ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%40HAT%7B%26sigma%3B%7D]()
= .
(f) A 95% confidence interval for the mean exam score of all students who study 12 hours is
( , ).
(g) A 95% prediction interval for the final exam score for a student who studies 12 hours is
( , ).
(h) A 95% confidence interval for the slope ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%26beta%3B%40SUB%7B1%7D]()
of the true regression line is ( , ).
(i) We would like to conduct a hypothesis test of H0: ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%26beta%3B%40SUB%7B1%7D]()
= 0 vs. Ha: ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%26beta%3B%40SUB%7B1%7D%26ne%3B]()
0 at the 5% level of significance. The value of the test statistic for the appropriate test of significance is t = .
(j) The P-value of the appropriate test of significance is between and .
(k) Use JMP to find the exact P-value of the test. The exact P-value (rounded to four decimal places) is .
(l) Using only the result in (i), what would be the value of the test statistic (rounded to two decimal places) if we had conducted this test using an analysis of variance? F =
(m) Using only the result in (k), what would be the P-value of the test (rounded to four decimal places) if we had conducted this test using an analysis of variance?
(n) What is the correct conclusion of the test?
|
Reject H0. There is sufficient evidence that Study Time and Exam Score do not a linear relationship.
|
|
|
|
|
|
|
|
|
Fail to reject H0. There is insufficient evidence that Study Time and Exam Score do not have a linear relationship.
|
|
|
|
|
|
|
|
|
Reject H0. There is sufficient evidence that Study Time and Exam Score have a linear relationship.
|
|
|
|
|
|
|
|
|
Fail to reject H0. There is sufficient evidence that Study Time and Exam Score have a linear relationship.
|
|
|
|
|
|
|
|
projectek
