Q. 57. Fish oil To see if fish oil can ... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 10: Q. 57. (page 669)

Fish oil To see if fish oil can help reduce blood pressure, males with high
blood pressure were recruited and randomly assigned to different treatments. Seven of the men were assigned to a 4-week diet that included fish oil. Seven other men were assigned to a 4-week diet that included a mixture of oils that approximated the types of fat in a typical diet. Each man鈥檚 blood pressure was measured at the beginning of the study. At the end of the 4 weeks, each volunteer鈥檚 blood pressure was measured again and the reduction in diastolic blood pressure was recorded. These differences are shown in the table. Note that a negative value means that the subject鈥檚 blood pressure increased.26
a. Do these data provide convincing evidence that fish oil helps reduce blood pressure more, on average, than regular oil?
b. Interpret the P-value from part (a) in the context of this study.

Short Answer

Expert verified

Part a) There is convincing evidence that fish oil helps reduce blood pressure more on average than regular oil.

Part b) There is $1.108 %$ the chance 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.

Step by step solution

Part a) Step 1: Given information

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

$伪 = 0.05$

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

Part a) Step 2: Explanation

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:

$H_{0} : 渭_{1} = 渭_{2} H_{0} : 渭_{1} > 渭_{2}$

Where,

$渭_{1} =$ the true mean reduction in blood pressure for subjects using fish oil.

$渭_{2} =$ the true mean reduction in blood pressure for subjects using regular oil.

Now, the mean is as follows:

role="math" localid="1655075713017" ${\overset{炉}{x}}_{1} = \frac{{鈭�}_{i = 1}^{n} x_{i}}{n} = \frac{8 + 12 + 10 + 14 + 2 + 0 + 0}{7} = 6.5714 {\overset{炉}{x}}_{2} = \frac{{鈭�}_{i = 1}^{n} x_{i}}{n} = \frac{- 6 + 0 + 1 + 2 - 3 - 4 + 2}{7} = - 1.1429$

And the standard deviation is as follows:

$s_{1} = 5.8554 s_{2} = 3.1848$

Locate the following test statistics:

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

Now, the degree of freedom will be:

$d f = m i n (n_{1} - 1, n_{2} - 1) = m i n (7 - 1, 7 - 1) = 6$

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

By the calculator, we calculate the $P$ -value that will be: $2 脳 tcdf (3.062, 1 E 99, 6)$ 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

$P < 0.05 鈬� Reject H_{0}$

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

Part b) Step 1: Explanation

From part (a)

We have,

$P < 0.05 鈬� Reject H_{0}$

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.