Answer:
The 95% confidence interval for the mean change in blood pressure, [tex]\bar{x}[/tex], is 1.744 < [tex]\bar{x}[/tex] < 2.816
Step-by-step explanation:
The parameters given are;
The number of people in the sample, n = 9
The average drop in blood pressure, [tex]\bar{x}[/tex] = 2.28 points
The standard deviation, σ = 0.82
The confidence level = 95%
The formula for confidence interval with a known mean is given as follows;
[tex]CI=\bar{x}\pm z_{\alpha/2} \dfrac{\sigma}{\sqrt{n}}[/tex]
Where:
[tex]z_{\alpha/2}[/tex] = z - score at 95% confidence level = 1.96
We therefore have;
[tex]CI=2.28 \pm 1.96 \times \dfrac{0.82}{\sqrt{9}}[/tex]
Which gives the 95% confidence interval for the mean change in pressure, [tex]\bar{x}[/tex], is given as follows;
1.744 < [tex]\bar{x}[/tex] < 2.816
