Question

# A fitness trainer claims that high intensity power training decreases the body fat percentages of females....

A fitness trainer claims that high intensity power training decreases the body fat percentages of females. The table below shows the body fat percentages of

eight

females before and after 10 weeks of high intensity power training. At

alphaαequals=0.10

is there enough evidence to support the​trainer's claim? Assume the samples are random and​ dependent, and the population is normally distributed. Complete parts​ (a) through​ (e) below.

 Female Body_Fat_%_(before) Body_Fat_%_(after) 1 27.2 27.1 2 23.6 23 3 23.9 23.8 4 23.5 23.4 5 24.2 24 6 27.4 26.8 7 28.3 28.2 8 28.1 28.5

​(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

What is the​ claim?

High intensity power training

decreases

the body fat percentages of females.

Let

mu Subscript dμd

be the hypothesized mean of the difference in the body fat percentages

​(beforeminus−​after).

What are

Upper H0

and

Upper H Subscript aHa​?

​(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.)

​(c) Calculate

d overbard

and

s Subscript dsd.

Calculate

s Subscript dsd.

​(d) Find the standardized test statistic t.    ​(e) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.

1) ____ the null hypothesis. There (2)_____ enough evidence to (3) ________ the claim that high intensity power training (4) _____ the body fat percentages of females.

(1) reject, fail to reject    (2) is, is not (3) reject, support (4) decreases, increases

8.

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