In a test of the effectiveness of garlic for lowering cholesterol, 47 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after thetreatment. The changes (before - after) in their levels of LDL cholesterol (in mg/dL) have a mean of 3.7 and a standard deviation of 18.2. Construct a 90% confidence interval estimate ofthe mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?Click here to view a t distribution table.Click here to view page 1 of the standard normal distribution table.Click here to view page 2 of the standard normal distribution table.What is the confidence interval estimate of the population mean p?Question Viewermg/dL < p< mg/dL(Round to two decimal places as needed.)What does the confidence interval suggest about the effectiveness of the treatment?O A. The confidence interval limits do not contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.O B. The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.O C. The confidence interval limits contain 0, suggesting that the garlic treatment did affect the LDL cholesterol levels.O D. The confidence interval limits do not contain 0, suggesting that the garlic treatment did affect the LDL cholesterol levels.

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Description: In a test of the effectiveness of garlic for lowering cholesterol, 47 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after thetreatment. The changes (before - after) in their levels of LDL c

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MATLAB: An Introduction with Applications

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In a test of the effectiveness of garlic for lowering cholesterol, 47 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the
treatment. The changes (before - after) in their levels of LDL cholesterol (in mg/dL) have a mean of 3.7 and a standard deviation of 18.2. Construct a 90% confidence interval estimate of
the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
Click here to view a t distribution table.
Click here to view page 1 of the standard normal distribution table.
Click here to view page 2 of the standard normal distribution table.
What is the confidence interval estimate of the population mean p?
Question Viewer
mg/dL < p< mg/dL
(Round to two decimal places as needed.)
What does the confidence interval suggest about the effectiveness of the treatment?
O A. The confidence interval limits do not contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
O B. The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
O C. The confidence interval limits contain 0, suggesting that the garlic treatment did affect the LDL cholesterol levels.
O D. The confidence interval limits do not contain 0, suggesting that the garlic treatment did affect the LDL cholesterol levels.

Expert Solution

Step 1

The sample size is 47, sample mean is 3.7, and standard deviation is 18.2.

The degrees of freedom is,

$\begin{array}{rcl} d f & = & n - 1 \\ = & 47 - 1 \\ = & 46 \end{array}$

The degrees of freedom is 46.

Computation of critical value:

The critical value of t-distribution at 46 degrees of freedom can be obtained using the excel formula “=T.INV.2T(0.10,46)”. The critical value is 1.6787.

The 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment is,

$\begin{array}{rcl} C I & = & {\bar{x}}_{d} \pm t_{\frac{α}{2}} (\frac{s_{d}}{\sqrt{n}}) \\ = & 3.7 \pm 1.6787 (\frac{18.2}{\sqrt{47}}) \\ = & 3.7 \pm 4.46 \\ = & (3.7 - 4.46, 3.7 + 4.46) \\ = & (- 0.76, 8.16) \end{array}$

Thus, the 90% confidence interval estimate of the population mean $μ$ is, -0.76 mg/dL < $μ$ < 8.16 mg/dl.

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