Respuesta :
Answer:
The 95 % confidence interval for the mean is between 28.09 and 35.97.
Step-by-step explanation:
Mean of the sample:
30 values.
So we sum all the values and divide by 30.
The sum of all the values(43 + 52 + 18 + ... + 20 + 41) is 961.
961/30 = 32.03
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{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
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 = 1.96\frac{11}{30} = 3.94[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 32.03 - 3.94 = 28.09
The upper end of the interval is the sample mean added to M. So it is 32.03 + 3.94 = 35.97
The 95 % confidence interval for the mean is between 28.09 and 35.97.
