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The systolic blood pressure measurements of a sample of 12 subjects are recorded as:鈥渂efore the drug Captopril is taken鈥� and 鈥渁fter the drug Captopril is taken鈥�.

It is claimed that the drug Captopril is effective in lowering systolic blood pressure levels.

Corresponding to the given claim, the following hypotheses are set up:

Null Hypothesis:

\({H_0}:{\mu _d} = 0\)

Alternative Hypothesis:

\({H_1}:{\mu _d} > 0\)

The test is right-tailed.

Where \({\mu _d}\)be the mean difference between the systolic blood pressure levels before and after taking the drug.

The following table shows the differences in the systolic blood pressure levels for each matched pair:

The mean value of the differences is computed below:

\(\begin{aligned} \bar d &= \frac{{\sum\limits_{i = 1}^n {{d_i}} }}{n}\\ &= \frac{{9 + 4 + ...... + 33}}{{12}}\\ &= 18.58\end{aligned}\)

The standard deviation of the differences is computed below:

\(\begin{aligned} {s_d} &= \sqrt {\frac{{\sum\limits_{i = 1}^n {{{({d_i} - \bar d)}^2}} }}{{n - 1}}} \\ &= \sqrt {\frac{{{{\left( {9 - 18.58} \right)}^2} + {{\left( {4 - 18.58} \right)}^2} + ....... + {{\left( {33 - 18.58} \right)}^2}}}{{12 - 1}}} \\ &= 10.10\end{aligned}\)

The mean value of the differences for the population of matched pairs \(\left( {{\mu _d}} \right)\) is considered to be equal to 0.

The value of the test statistic is computed as shown:

\(\begin{aligned} t &= \frac{{\bar d - {\mu _d}}}{{\frac{{{s_d}}}{{\sqrt n }}}}\\ &= \frac{{18.58 - 0}}{{\frac{{10.10}}{{\sqrt {12} }}}}\\ &= 6.371\end{aligned}\)

The degrees of freedom are computed below:

\(\begin{aligned} df &= n - 1\\ &= 12 - 1\\ &= 11\end{aligned}\)

The critical value of t at\(\alpha = 0.01\)and degrees of freedom equal to 11 for a right-tailed test is equal to 2.7181.

The corresponding p-value is equal to 0.00003.