Question

A researcher claims that a​ post-lunch 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​ post-lunch nap and when they did take a​ post-lunch 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​ post-lunch 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​ post-lunch 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 nappost-lunch nap

▼

decreases

increases

the amount of time it takes males to sprint 20 meters.

Click to select your answer(s).

Answer 1

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.