Question

# A researcher claims that a​ post-lunch nap decreases the amount of time it takes males to...

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 3.99 4.02 3.98 4.01 3.97 3.92 3.92 4.07 3.98 3.98 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.

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.

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