Question

19. James has a desk job and would like to become more fit, so he purchases a

tread walker and a standing desk which will allow him to walk at a slow pace as
he works. However, he is concerned that standing and walking while working
may cause his productivity to decline. After working this way for 6 months he
takes a simple random sample of 15 days.
He records how long he walked that day (in hours) as recorded by his fitness watch as
well as his billable hours for that day as recorded by a work app on his computer.
Regression Analysis: Billable hours versus Walk time
Predictor
Constant
Walk time
P
Coef
7.785
-0.245
SE Coef
0.542
0.205
1
14.363
-1.195
0.000
0.127
Assuming that all conditions for inference are met, which of the following is a 95
percent confidence interval for the average change in the number of billable hours for
each increase of 1 hour spent walking?
(A) -0.245 $ 1.960(0.205)
(B) -0.245 + 2.131(0.205)
(C) -0.245 = 2.160(0.205)
(D) 7.785 † 1.960(0.542)
(E) 7.785 + 2.160(0.542)​

Answer 1

The correct answer is option (C)-0.245 = 2.160(0.205)

Explanation:

Solution

Given that:

The slope = - 0.245

The size sample = n = 15

The standard error = 0.205

The confidence level = 95

The Significance level= α = (100- 95)% = 0.05

Now,

The freedom of degree = n-2 = 15 -2= 13

Thus,

the critical value = t* = 2.16

By applying Excel = [TINV (0.05, 13)]

The Margin of error is = t* (standard error)

=2.16 *0.205

= 0.4428