Respuesta :
Answer:
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.
Step-by-step explanation:
The first step is finding the sample mean, which is the sum of all 14 blood pressures, divided by 14. So
[tex]S = \frac{128 + 121 + 129 + 128 + 123 + 137 + 138 + 147 + 122 + 144 + 125 + 140 + 134 + 125}{14}[/tex]
[tex]S = 131.5[/tex]
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575\frac{9}{\sqrt{14}} = 6.2[/tex]
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.
