Q. 91 91. A powder diet is tested on 4... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 10: Q. 91 (page 602)

91. A powder diet is tested on $49$ people, and a liquid diet is tested on $36$ different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of $42$ pounds with a standard deviation of $12$ pounds. The liquid diet group had a mean weight loss of $45$ pounds with a standard deviation of $14$ pounds.

Short Answer

Expert verified

(a) The null hypothesis: $H_{0} : 渭_{1} 鈮� 渭_{2}$
(b) The alternate hypothesis: $H_{a} : 渭_{1} > 渭_{2}$
(c) The random variable is the difference in mean weight loss between the liquid and powder diets.
(d) Student's t distribution.
(e) The test statistics: $- 1.036$ .
(f) The $p$ -value is $0.15189$ .
(g) (i) $伪 = 0.05$
(ii) Decision: Null hypothesis is not rejected.
(iii) $伪 < p$ -value
(iv) As a result, there is not enough proof to conclude that the liquid diet yields a more weight loss than the powder diet, at the $5 %$ level of significance .

Step by step solution

Given information

The powder diet group had a mean weight loss of $42$ pounds with a standard deviation of $12$ pounds. The liquid diet group had a mean weight loss of $45$ pounds with a standard deviation of $14$ pounds.

Explanation

(a) The null hypothesis is described as follows:
$H_{0} : 渭_{1} 鈮� 渭_{2}$
(b)The alternate hypothesis is described as follows:
$H_{a} : 渭_{1} > 渭_{2}$
(c) The random variable is the difference in mean weight loss between the liquid and powder diets.
(d) Student's t distribution.
(e) To determine test static as follows:
To enter the stat list editor, press STAT followed by $1$ .

Then, ENTER all the values the OUTPUT will be:

Hence the test statistics is $- 1.036$ .

Explanation

(f) The $p$ value is determined from the output as $0.15189$ .
(g) Using the data from the last exercise, create a mental picture of the situation.
The horizontal axis should be clearly labelled and scaled, and the region(s) matching to the $p$ -value should be shaded on the graph.

(i) $伪 = 0.05$
(ii) Decision: Null hypothesis is not rejected.
(iii) $伪 < p$ -value
(iv) As a result, there is not enough proof to conclude that the liquid diet yields a more weight loss than the powder diet, at the $5 %$ level of significance.