Scenario (High Pressure Situation): More than a 1000 miltion odustin the United States have high bleod pressure. A study investigates the effect of a new anthipertenstive medication on systolic blood pressure. Researchers randomly selected 10 patients diagnosed with high blood pressure and measured their systolic blood pressure before starting medication. After 8 weeks of toking the nea mediectien. the patients' systolic blood pressure was measured again. The researchers calculate the difference in blood pressure for each patient (before minus after). A dot plot of the differences indicated that the mean of the differences was normally distributed. Before & 150 & 160 & 145 & 155 & 148 & 152 & 160 & 155 & 158 & 150 & 5=5.1434 After & 133 & 142 & 131 & 140 & 133 & 140 & 145 & 140 & 142 & 136 & 5=4.6619 Determine at the 01 significance level whether or not the medication is effective in lowering systolic blood pressure. Label/List a) mu= b) s_(x)= Formula c) bar(x)= d) n= Inference Procedure t=(bar(x) d-M d)/(sqrt(frac(s)(n))) Hypothesis Ho: M=0 HA:M 0

To determine whether the new antihypertensive medication is effective in lowering systolic blood pressure at the 0.01 significance level, you can perform a one-sample t-test on the differences in blood pressure before and after taking the medication. Here are the steps to follow:<br /><br />1. **State the Hypotheses:**<br /> - Null Hypothesis (\(H_0\)): The mean difference in systolic blood pressure (before minus after) is zero. This implies that the medication has no effect.<br /> - Alternative Hypothesis (\(H_a\)): The mean difference in systolic blood pressure is greater than zero. This implies that the medication is effective in lowering blood pressure.<br /><br />2. **Significance Level:**<br /> - \(\alpha = 0.01\)<br /><br />3. **Calculate the Test Statistic:**<br /> - Use the formula for the t-statistic: <br /> \[<br /> t = \frac{\bar{d} - \mu_0}{s_d / \sqrt{n}}<br /> \]<br /> where \(\bar{d}\) is the sample mean of the differences, \(\mu_0\) is the hypothesized population mean difference (0 in this case), \(s_d\) is the standard deviation of the differences, and \(n\) is the sample size.<br /><br />4. **Determine the Critical Value:**<br /> - For a one-tailed test at the 0.01 significance level with \(n-1\) degrees of freedom, find the critical t-value from the t-distribution table.<br /><br />5. **Make a Decision:**<br /> - If the calculated t-statistic is greater than the critical t-value, reject the null hypothesis. Otherwise, do not reject the null hypothesis.<br /><br />6. **Conclusion:**<br /> - Based on the decision, conclude whether there is sufficient evidence to suggest that the medication is effective in lowering systolic blood pressure at the 0.01 significance level.