Question

When fourteen different second-year medical students measured the blood pressure of the same person, they obtained the result listed below. Assuming that the population standard deviation is known to be 9, construct and interpret a 99% confidence interval estimate of the population mean.

Data: 128 121 129 128 123 137 138 147 122 144 125 140 134 125

Answer 1

The 99% confidence interval estimate of the population mean is between 125.3 and 137.7. This means that we are 99% sure that the true population mean, that is, the mean blood pressure of all second-year medical students, is in this interval.

Explanation:

The first step is finding the sample mean, which is the sum of all 14 blood pressures, divided by 14. So

`S = (128 + 121 + 129 + 128 + 123 + 137 + 138 + 147 + 122 + 144 + 125 + 140 + 134 + 125)/(14)`

`S = 131.5`

Confidence interval:

We have that to find our
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1 - 0.99)/(2) = 0.005`

Now, we have to find z in the Ztable as such z has a pvalue of
`1 - \alpha`.

That is z with a pvalue of
`1 - 0.005 = 0.995`, so Z = 2.575.

Now, find the margin of error M as such

`M = z(\sigma)/(√(n))`

In which
`\sigma` is the standard deviation of the population and n is the size of the sample.

`M = 2.575(9)/(√(14)) = 6.2`

The lower end of the interval is the sample mean subtracted by M. So it is 131.5 - 6.2 = 125.3

The upper end of the interval is the sample mean added to M. So it is 131.5 + 6.2 = 137.7

The 99% confidence interval estimate of the population mean is between 125.3 and 137.7. This means that we are 99% sure that the true population mean, that is, the mean blood pressure of all second-year medical students, is in this interval.