Question

The mean diastolic blood pressure for a random sample of 80 people was 100 millimeters of mercury. If the standard deviation of individual blood pressure readings is known to be 11 millimeters of mercury, find a 95% confidence interval for the true mean diastolic blood pressure of all people. Then give its lower limit and upper limit.

Answer 1

The confidence interval for the true mean diastolic blood pressure of all people is 100 ± 2.41 where the lower limit is 97.59 and the upper limit is 102.41

How to determine the confidence interval?

We have:

Mean = 100

Sample size = 80

Standard deviation = 11

At 95% confidence interval, the critical z value is:

z = 1.96

The confidence interval is then calculated as:

$CI = \bar x \pm z \frac{\sigma}{\sqrt n}$

So, we have:

$CI = 100 \pm 1.96 \frac{11}{\sqrt {80}}$

Evaluate the product

$CI = 100 \pm \frac{21.56}{\sqrt {80}}$

Divide

$CI = 100 \pm 2.41$

Split

CI  = (100 - 2.41,100 + 2.41)

Evaluate

CI  = (97.59,102.41)

Hence, the confidence interval for the true mean diastolic blood pressure of all people is 100 ± 2.41

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