Question

For a sample of 116 college students, the relationship between the reported hours of sleep during the previous 24 hours and the reported hours of study during the same period was studied. Data for y = hours of sleep the previous day and x = hours of studying the previous day for n = 116 college students were computed. Some regression results for those data are shown in the following table.

Regression output
Predictor	Coef	SE Coef	T	P
Constant	7.5551	0.2236	33.79	0.000
study	-0.2779	0.6503	-0.43	0.341
S = 1.509 R-Sq = 9.62%

(a) What is the value of the slope of the regression line? On your paper, write a sentence that interprets this number.


(b) What is the value of the correlation coefficient? Round your answer to two decimal places.


(c) What percent of the variation in sleep time is due to the variation in study time? You must round your answer to two decimal places.
%

(d) Calculate the predicted value of hours of sleep the previous day for a student who studied 4 hours the previous day. You must round your answer to three decimal places.

(e) To test whether the relationship between study hours and sleep is significant, which hypotheses are appropriate? Select all that apply.

H₀:

The population y-intercept = 0 vs.

H_a:

The population y-intercept is nonzero

H₀:

The population slope = 0 vs.

H_a:

The population slope is nonzero

H₀: μ₁ − μ₂ = 0

vs.

H₀: μ₁ − μ₂ ≠ 0

H₀:

The variables are not related vs.

H_a:

The variables are related


(f) If we assume that conditions are met, the test statistic value is T =
and the p-value is

Between 0.01 and 0.05 Greater than 0.05    Less than 0.01

(g) An appropriate and complete conclusion is:

We reject the null hypothesis. There is no significant relationship between sleep time and study time.We reject the null hypothesis. There is a significant relationship between sleep time and study time.    We fail to reject the null hypothesis. There is a significant relationship between sleep time and study time.We fail to reject the null hypothesis. There is no significant relationship between sleep time and study time.

Answer 1

a)  
slope=   -0.2779
for every 1 hours increase of studying the previous day, hours of sleep the previous day get decrease by 0.2779  
  
b)  
value of r =     -0.98
  
c) 9.62%

d)  
Y^=7.5551-0.2779*4=   6.444

e)

H0:

The population slope = 0 vs.

Ha:

The population slope is nonzero

f)

T=-0.43

p value > 0.05

g) We fail to reject the null hypothesis. There is no significant relationship between sleep time and study time.