Question

An experiment is conducted to show that blood pressure can be consiously reduced in people trained in a " biofeedback exercise program" six subjects were randomly selected and blood pressure measurements were recorded before and after the training. the difference between the pleasure was calculated producing the following results; ${\overline{x}}_d=-10.2s_d=8.4$using the data, test the hypothesis that the blood pressure has decreased after the training.

If $\alpha =0.05$,the P value and the conclusions are

a.$0.0014$; There is sufficient evidence to conclude that the blood pressure has decreased after the training.

b. $0.0014$; There is sufficient evidence to conclude that the blood pressure has increased after the training.

c. $0.0155$; There is sufficient evidence to conclude that the blood pressure has decreased after the training.

d.$0.0155$; There is sufficient evidence to conclude that the blood pressure has increased after the training.

Short answer

The correct option is |(c).

$0.0155$; There is sufficient evidence to conclude that the blood pressure has decreased after the training.

Step-by-step solution

Given Information

Given in the question that

$H_0:{\mu }_d=0$

$H_0:{\mu }_d\ne 0$

$n=5$

$\overline{x_d}=10.2$

$s_d=8.4$

We have to determine that the blood pressure has decreased after the training.

Explanation

The formula of test statistic is:

$$\begin{gathered} tstat=\frac{d-\mu d}{\frac{sd}{\sqrt{n}}} \\ =\frac{-10.2-0}{\frac{8.4}{\sqrt{5}}} \\ =2.72 \end{gathered}$$

$\alpha =0.05$

Degree of freedom can be calculated as

$$\begin{gathered} DOF=n-1 \\ =5-1 \\ =4 \end{gathered}$$

P value can be calculated as

$$\begin{gathered} Pvalue=P\left(\right|t|<to) \\ =P\left(\right|t|<2.72) \\ =0.0155 \end{gathered}$$

By using t table P value $<0.05$

Therefore we reject null hypothesis.

Hence, There is sufficient evidence to conclude that the blood pressure has decreased after the training.