Chapter 10, Problem 31PT3

To determine

To test whether the dieters is managed to not to regain the weight they lost.

Explanation of Solution

Given the following information:

Given the weight of person before diet and after diet in pounds.

The test procedure:

The null and alternative hypothesis is given by

  $\begin{array}{l}{H}_0:{\mu }_d=0\\ H_1:{\mu }_d>0\end{array}$

Where ${\mu }_d\text{ is the mean of the deviation}\text{.}$

The test statistic is given by,

  $\begin{array}{l}t=\frac{\overline{d}}{Sd(\overline{d})}~t_{n-1}\\ \text{where }\overline{d}\text{ is the mean of the deviation in the paired sanple}\end{array}$

Reject the null hypothesis if $t>t_{\alpha },n-1$

Calculation:

before x	after y	d = x-y
158	163	-5
185	182	3
176	188	-12
172	150	22
164	161	3
234	220	14
258	235	23
200	191	9
228	228	0
246	237	9
198	209	-11
221	220	1
236	222	14
255	268	-13
231	234	-3

Mean of d	3.6
SD of d	11.52513
t	0.312361
t cri	1.76131

The above table is obtained from excel.

The value of test statistic t = 0.312361

Critical value of t at 0.05 level of significance = 1.76131

As t <1.76131, we do not reject the null hypothesis and conclude that the five-week crash diet is not effective over a long period of time.