91Ó°ÊÓ

Given in the question that, an experiment is conducted to show that blood pressure can be consciously 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 blood pressures was calculated (after - before) producing the following results: ${\stackrel{¯}{x}}_d=-10.2{\mathrm{s}}_d=8.4$. Using the data, test the hypothesis that the blood pressure has decreased after the training.

118. The distribution for the test is:

a.$t_5$

b. $t_6$

c.$N(-10.2,8.4)$

d.$\mathrm{N}\left(-10.2,\frac{8.4}{\sqrt{6}}\right)$

We know that,

$$\begin{gathered} {\stackrel{¯}{x}}_d=-10.2 \\ {\mathrm{s}}_d=8.4 \end{gathered}$$

So, lets find the test statistics:

localid="1655118365187" $$\begin{gathered} \text{t}=\frac{d-\mathrm{μ}d}{\frac{sd}{\sqrt{n}}} \\ =\frac{-10.2-0}{\frac{8.4}{\sqrt{5}}} \\ =-2.72 \end{gathered}$$

Let's find the $p$value:

localid="1655118432909" role="math" $$\begin{gathered} \text{pvalue}=P(t<\left|t\right|) \\ =\mathrm{P}(t<2.72) \\ =0.0155 \end{gathered}$$

The paired test, often known as the paired t-test, is utilised and follows the $t$distribution with $n-1$degrees of freedom. Assume $n=6$and a $5$degrees-of-freedom t distribution.

$\left(a\right)$is the answer.