Question

Question: 9 hypertension patients in a clinic use an experimental drug for treatment. The systolic blood pressure reading for these patients before and after using the drug are as follows:

Assume that blood pressure has a standard deviation of 5 mmHg. Do you think the drug works?

ID	BP BEFORE (mmHg)	BF AFTER (mmHg)
1	145	138
2	140	142
3	150	140
4	142	148
5	155	151
6	152	140
7	148	132
8	160	160
9	152	148

After solving the problem;

1-) Choose the treshold value on your own.

2-) Explain briefly why you choose that numbers as treshold

3-) Make comments on the result of hypothesis test.

Thank you for everything.

Answer 1

1) To test this hypothesis, we can choose the 5% level of significance as the threshold value.

2) The reason for selecting the above threshold value is universality. Most of the hypothesis test use the significance level at 5% because of it the moderate between 1% and 10%.

3) The above analysis is performed in Excel and steps are as follows-

z-Test: Two-Sample for Means in excel

I performed the analysis using basic commands in MS Excel and I am giving the steps to be followed-

1. Select the Data tab and choose the Data Analysis in the top right-hand corner

2. In the Data Analysis menu choose z-Test: Two-Sample for Means: Single Factor and click OK

3. In the ‘Input Range’ box, select all the data in the columns you created, including the variable names

4. Check the ‘Labels in First Row’ box

5. In the ‘Output Range’ box, enter a cell range where Excel will place the output and click OK

6. If the p-value were less than 0.05, you would reject the null hypothesis that says the means of all categories are equal. If the p-value were greater than 0.05, then you would fail to reject the null.

The results are followed-

Conclusion: Since the test is the improvement of blood pressure after taking the drug so the hypothesis should be that the blood pressure is lowered after taking the drug. that's sound like a one-tailed test.

Now the p-value is 0.017 for one-tailed which less than 0.05 so we have enough evidence to reject the null hypothesis of no improvement. We conclude that after taking the drug there is significant improvement in the high blood pressure.