Question

 

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 ten weeks of high-intensity power training. At

alphaαequals=0.01

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	1	2	3	4	5	6	7	8
Body fat percentage​(before)	23.8	24.2	26.5	24.9	28.8	22.9	24.5	23.9
Body fat percentage​ (after)	20.4	20.9	23.9	22.6	23.7	22.8	19.6	24.1

​(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

What is the​ claim?

High intensity power training __________ (increases/decreases, does not affect, affects/).

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.

d overbardequals=____

​(Round to three decimal places as​ needed.)

Calculate

s Subscript dsd.

s Subscript dsdequals=_________

​(Round to three decimal places as​ needed.)

​(d) Find the standardized test statistic t.

tequals=________

​(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.

(1)

the null hypothesis. There

(2)

enough evidence to

(3)

the claim that high intensity power training

(4)

the body fat percentages of females.

Answer 1

A) High intensity power training decreases.

H₀: = 0

H1: > 0

B) At alpha = 0.01, the critical value is t^* = 2.998

Reject H₀: if t > 2.998

C) = (3.4 + 3.3 + 2.6 + 2.3 + 5.1 + 0.1 + 4.9 + (-0.2))/8 = 2.687

s_d = sqrt(((3.4 - 2.687)^2 + (3.3 - 2.687)^2 + (2.6 - 2.687)^2 + (2.3 - 2.687)^2 + (5.1 - 2.687)^2 + (0.1 - 2.687)^2 + (4.9 - 2.687)^2 + (-0.2 - 2.687)^2)/7) = 1.956

D) The test statistic t = (- D)/(s_d/)

= (2.687 - 0)/(1.956/) = 3.885

E) Since the test statistic value is greater than the critical value (3.885 > 2.998), so we should reject the null hypothesis.

Reject the null hypothesis. There is enough evidence to the claim that the high intensity power training decreases the body fat percentages of females.