Question

A weight loss program is announced by Health fitness centre claiming weight loss for sure. A random sample of eight recent participants showed the following weights before and after completing the course. At the 0.01 significance level, can we conclude the students lost weight?

Names	Before	After
Hunter	157	153
Cashman	225	209
Mervine	141	147
Massa	152	147
Creola	201	186
Perterson	154	140
Redding	174	160
Poust	185	175

(a) State the null hypothesis and the alternative hypothesis.

(b) What is the critical value of t?

(c) What is the computed value of t?

(d) Interpret the result. What is the p-value?

(e) What assumption needs to be made about the distribution of the differences?

Answer 1

Before	After	Difference
157	153	4
225	209	16
141	147	-6
152	147	5
201	186	15
154	140	14
174	160	14
185	175	10

∑x = 72 , ∑x² = 1050, n = 8

Mean , x̅d = Ʃx/n = 72/8 = 9

Standard deviation, sd = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(1050-(72)²/8)/(8-1)] = 7.5782

a) Null and Alternative hypothesis:

Ho : µd = 0

H1 : µd > 0

b) df = n-1 = 7

Critical value :

Right tailed critical value, t-crit = ABS(T.INV(0.01, 7)) = 2.998

Reject Ho if t > 2.998

c) Test statistic:

t = (x̅d)/(sd/√n) = (9)/(7.5782/√8) = 3.359

d) p-value :

p-value = T.DIST.RT(3.3591, 7) = 0.0060

Decision:

p-value < α, Reject the null hypothesis

e) Assumptions:

• The observations are independent of one another.
• The dependent variable should be approximately normally distributed.
• The dependent variable should not contain any outliers.
• The dependent variable must be continuous (interval/ratio).