Respuesta :
Answer:
The 95% confidence interval for the population mean is between $20.51 and $24.21.
Step-by-step explanation:
The first step to find this question is find the sample mean
[tex]\mu_{x} = \frac{22.10 + 23.25 + 21.35 + 24.50 + 21.90 + 20.75 + 22.65}{7} = 22.36[/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{1-0.95}{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 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{2.5}{\sqrt{7}} = 1.85[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 22.36 - 1.85 = $20.51
The upper end of the interval is the sample mean added to M. So it is 22.36 + 1.85 = $24.21
The 95% confidence interval for the population mean is between $20.51 and $24.21.
