A researcher claims that a postlunch nap decreases the amount of time it takes males to sprint 20 meters after a night with only 4 hours of sleep. The table shows the amounts of time (in seconds) it took for 10 males to sprint 20 meters after a night with only 4 hours of sleep when they did not take a postlunch nap and when they did take a postlunch nap. At
alphaαequals=0.01,
is there enough evidence to support the researcher's claim? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (e) below.
Male 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 


Sprint time (without nap) 
3.99 
4.02 
3.98 
4.01 
3.97 
3.92 
3.92 
4.07 
3.98 
3.98 

Sprint time (with nap) 
3.97 
4.01 
3.95 
4.04 
3.94 
3.91 
3.93 
4.06 
3.97 
3.95 
(a) Identify the claim and state
Upper H 0H0
and
Upper H Subscript aHa.
What is the claim?
A.
A night with only 4 hours of sleep decreases the amount of time it takes males to sprint 20 meters.
B.
A postlunch nap decreases the amount of time it takes males to sprint 20 meters.
C.
A night with only 4 hours of sleep increases the amount of time it takes males to sprint 20 meters.
D.
A postlunch nap increases the amount of time it takes males to sprint 20 meters.
Let
mu Subscript dμd
be the hypothesized mean of the difference in the sprint times (without
napminus−with
nap). What are
Upper H 0H0
and
Upper H Subscript aHa?
A.
Upper H 0H0:
mu Subscript dμdgreater than or equals≥d overbard
Upper H Subscript aHa:
mu Subscript dμdless than<d overbard
B.
Upper H 0H0:
mu Subscript dμdgreater than or equals≥0
Upper H Subscript aHa:
mu Subscript dμdless than<0
C.
Upper H 0H0:
mu Subscript dμdnot equals≠0
Upper H Subscript aHa:
mu Subscript dμdequals=0
D.
Upper H 0H0:
mu Subscript dμdequals=0
Upper H Subscript aHa:
mu Subscript dμdnot equals≠0
E.
Upper H 0H0:
mu Subscript dμdless than or equals≤d overbard
Upper H Subscript aHa:
mu Subscript dμdgreater than>d overbard
F.
Upper H 0H0:
mu Subscript dμdless than or equals≤0
Upper H Subscript aHa:
mu Subscript dμdgreater than>0
(b) Find the critical value(s) and identify the rejection region(s).
Select the correct choice below and fill in any answer boxes to complete your choice.
(Round to three decimal places as needed.)
A.
tless than<nothing
B.
tless than<nothing
or
tgreater than>nothing
C.
tgreater than>nothing
(c) Calculate
d overbard
and
s Subscript dsd.
d overbardequals=nothing
(Round to three decimal places as needed.)Calculate
s Subscript dsd.
s Subscript dsdequals=nothing
(Round to three decimal places as needed.)
(d) Find the standardized test statistic t.
tequals=nothing
(Round to three decimal places as needed.)
(e) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.
▼
Reject
Fail to reject
the null hypothesis. There
▼
is not
is
enough evidence to
▼
support
reject
the claim that a
▼
night with only 4 hours of sleepnight with only 4 hours of sleep
post dash lunch nappostlunch nap
▼
decreases
increases
the amount of time it takes males to sprint 20 meters.
Click to select your answer(s).
e)
since, t < 1.833 we fail to reject the null hypothesis.
There is no enough evidence to support the claim that a night with only 4 hours sleepnight of sleep post lunch nap decreases the amount of time it take males to Sprint 20 meters.
Get Answers For Free
Most questions answered within 1 hours.