91Ó°ÊÓ

Ten individuals went on a low–fat diet for 12 weeks to lower their cholesterol. The data are recorded in Table 10.30. Do you think that their cholesterol levels were significantly lowered?

$\begin{array}{|ll|}\hline \text{Starting cholesterol level}& \text{Ending cholesterol level}\\ 140& 140\\ 220& 230\\ 110& 120\\ 240& 220\\ 200& 190\\ 180& 150\\ 190& 200\\ 360& 300\\ 280& 300\\ 260& 240\\ \hline\end{array}$

Use the following information to answer the next two exercises. A new AIDS prevention drug was tried on a group of 224 HIV positive patients. Forty-five patients developed AIDS after four years. In a control group of 224 HIV positive patients, 68 developed AIDS after four years. We want to test whether the method of treatment reduces the proportion of patients that develop AIDS after four years or if the proportions of the treated group and the untreated group stay the same.

Let the subscript $t=$treated patient and $ut=$untreated patient.

Step by step solution

01

Given Information 

Given in the question that,

$\begin{array}{|ll|}\hline \text{Starting cholesterol level}& \text{Ending cholesterol level}\\ 140& 140\\ 220& 230\\ 110& 120\\ 240& 220\\ 200& 190\\ 180& 150\\ 190& 200\\ 360& 300\\ 280& 300\\ 260& 240\\ \hline\end{array}$

02

Explanation 

The null hypothesis is defined as follows:

$H_0:{\mathrm{μ}}_d=0$

The following is an alternative hypothesis:

$H_0:{\mathrm{μ}}_d<0$

The mean difference in cholesterol levels is the random variable.

The distribution of students.

Fill in all requirements using Minitab's two sample $t$test option.

After we have entered all of the values, we will' get the following result.

The value of test statistics is: localid="1654021055728" $1.17$

The value of localid="1654021065369" $P$is: localid="1654021074185" $0.865$

The graph of the p value is shown below:

Here, $\mathrm{Î\pm }=0.05$

We can accept the null hypothesis. Because $p-\text{value}<\mathrm{Î\pm }$.

There is insufficient data to determine that the drug reduced cholesterol levels after 12 weeks at the 5 percent threshold of significance.

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