Question

The mean diastolic blood pressure for a random sample of 70 people was 94 millimeters of mercury. if the standard deviation of individual blood pressure readings is known to be 12 millimeters of mercury, find a 90% confidence interval for the true mean diastolic blood pressure of all people.

Answer 1

To solve this problem, we make use of the formula for Confidence Interval:

Confidence Interval = X ± z * σ / sqrt (n)

where X is the mean value, z is the z score which is taken from the standard tables, σ is the standard deviation, and n is the number of samples

z = 1.645 (at 90% Confidence Level)

Substituting the values into the equation:

Confidence Interval = 94 ± 1.645 * 12 / sqrt (70)

Confidence Interval = 94 ± 2.36

Confidence Interval = 91.64, 96.36

Therefore at 90% confidence level, the blood pressure reading ranges from 91.64 mmHg to 96.36 mmHg.