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.

*H*_{0}:

The population y-intercept = 0 vs.

*H*_{a}:

The population y-intercept is nonzero

*H*_{0}:

The population slope = 0 vs.

*H*_{a}:

The population slope is nonzero

*H*_{0}: *μ*_{1} −
*μ*_{2} = 0

vs.

*H*_{0}: *μ*_{1} −
*μ*_{2} ≠ 0

*H*_{0}:

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.

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