91Ó°ÊÓ

The researcher wants to know whether fish oil helps reduce blood pressure more than regular oil or not in this study.

$\mathrm{Î\pm }=0.05$

The given claim that: Mean is higher for the fish oil.

Now we must determine the most appropriate hypotheses for a significance test.

As a result, either the null hypothesis or the alternative hypothesis is the claim. According to the null hypothesis, the population proportions are equal. If the claim is the null hypothesis, the alternative hypothesis is the polar opposite of the null hypothesis.

The appropriate hypotheses for this are:

$$\begin{gathered} H_0:{\mathrm{μ}}_1={\mathrm{μ}}_2 \\ {H}_0:{\mathrm{μ}}_1>{\mathrm{μ}}_2 \end{gathered}$$

Where,

${\mathrm{μ}}_1=$the true mean reduction in blood pressure for subjects using fish oil.

${\mathrm{μ}}_2=$the true mean reduction in blood pressure for subjects using regular oil.

Now, the mean is as follows:

role="math" localid="1655075713017" $$\begin{gathered} {\stackrel{¯}{x}}_1=\frac{\underset{i=1}{\overset{n}{∑}}{x}_i}{n} \\ =\frac{8+12+10+14+2+0+0}{7} \\ =6.5714 \\ {\stackrel{¯}{x}}_2=\frac{\underset{i=1}{\overset{n}{∑}}{x}_i}{n} \\ =\frac{-6+0+1+2-3-4+2}{7} \\ =-1.1429 \end{gathered}$$

And the standard deviation is as follows:

$$\begin{gathered} s_1=5.8554 \\ {s}_2=3.1848 \end{gathered}$$

Locate the following test statistics:

$$\begin{gathered} =\frac{6.5714-(-1.1429)-0}{\sqrt{\frac{5.{8554}^2}{7}+\frac{3.{1848}^2}{7}}} \\ =3.062 \end{gathered}$$

Now, the degree of freedom will be:

$$\begin{gathered} df=min(n_1-1,n_2-1) \\ =min(7-1,7-1) \\ =6 \end{gathered}$$

So the P-value will be: $0.01<P<0.02$

By the calculator, we calculate the $P$-value that will be: $2×tcdf(3.062,1\mathrm{E}99,6)$which results in the P-value of $0.01108$

And we know that if the $P$-value is less than or equal to the significance level then the null hypothesis is rejected, then

$P<0.05⇒\text{Reject}{H}_0$

Therefore, we conclude that there is convincing evidence that fish oil helps reduce blood pressure more on average than regular oil.

From part (a)

We have,

$P<0.05⇒\text{Reject}{H}_0$

Hence, we came to the conclusion that fish oil reduces blood pressure more effectively than regular oil on average.

Therefore, we can say that there is $1.108\%$thechance of obtaining similar results or more extreme when the mean reduction in blood pressure is the same for those using fish oil and those using regular oil.