Can I get some help on problem 2 A-C Problem 2: Unlike drugs, vitamins and supplements are not regulated by the Food and DrugAdministration (FDA). Therefore vitamin and supplement companies can say anything theywant on their product without afraid of getting sued. However, most doctors believe that takingfish oil can truly help reduce bad cholesterol. Adults with cholesterol levels at or above200mg/dl are considered at risk of developing heart disease. A health clinic is testing a new fishoil by randomly selecting 41 at risk adults. They are told to take one fish oil pill per day for sixmonths. After six months, the clinic draws blood from these people to test for cholesterol. Themean cholesterol of these 41 adults is 192 mg/dl, with a standard deviation of 25 mg/dl.a) Do we have some evidence to suggest that this fish oil helps reduce cholesterol? Explain.b) Perform a hypothesis test at a significance level, alpha = 0.05. (Hint: after writing the Ho, andHa, translating them into English can help you understand better).c) Based on the test result from part b), what do recommend people with high cholesterol to do?

Name: Can I get some help on problem 2 A-C Problem 2: Unlike drugs, vitamins
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Description: Can I get some help on problem 2 A-C Problem 2: Unlike drugs, vitamins and supplements are not regulated by the Food and DrugAdministration (FDA). Therefore vitamin and supplement companies can say anything theywant on their product without afraid of

Answered: a) Do we have some evidence to suggest…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Can I get some help on problem 2 A-C

Problem 2: Unlike drugs, vitamins and supplements are not regulated by the Food and Drug
Administration (FDA). Therefore vitamin and supplement companies can say anything they
want on their product without afraid of getting sued. However, most doctors believe that taking
fish oil can truly help reduce bad cholesterol. Adults with cholesterol levels at or above
200mg/dl are considered at risk of developing heart disease. A health clinic is testing a new fish
oil by randomly selecting 41 at risk adults. They are told to take one fish oil pill per day for six
months. After six months, the clinic draws blood from these people to test for cholesterol. The
mean cholesterol of these 41 adults is 192 mg/dl, with a standard deviation of 25 mg/dl.
a) Do we have some evidence to suggest that this fish oil helps reduce cholesterol? Explain.
b) Perform a hypothesis test at a significance level, alpha = 0.05. (Hint: after writing the Ho, and
Ha, translating them into English can help you understand better).
c) Based on the test result from part b), what do recommend people with high cholesterol to do?

Expert Solution

Step 1

Given,

$n = 41 x = 192 s = 25 μ_{0} = 200 α = 0.05$

1). Since the mean cholesterol level of 41 adults after taking one fish pill per day for six months is less than the mean cholesterol for developing risk of heart disease, therefore there is some evidence to suggest that this fish oil helps reduce cholesterol.

2). The hypothesis to be tested here is-

$H_{0} : μ < 200 (T h e r e i s n o r i s k o f d e v e l o p i n g h e a r t d i s e a s e) H_{1} : μ \geq 200 (T h e r e i s r i s k o f d e v e l o p i n g h e a r t d i s e a s e)$

This is a right tailed test.

The test statistics is obtained as-

$\begin{array}{rcl} t & = & \frac{x - μ_{0}}{\frac{s}{\sqrt{n}}} \\ = & \frac{192 - 200}{\frac{25}{\sqrt{41}}} \\ = & - 2.049 \end{array}$

The degrees of freedom is obtained as-

$\begin{array}{rcl} d f & = & n - 1 \\ = & 41 - 1 \\ = & 40 \end{array}$

As per t-distribution table, the critical value of t at 0.05 level of significance for 40 degrees of freedom is obtained as 1.684.

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