Answer:
The 90% confidence interval for the population mean test score is between 66.54 and 75.46.
Step-by-step explanation:
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 - 0.9}{2} = 0.05[/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 - 0.05 = 0.95[/tex], so Z = 1.645.
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 = 1.645\frac{13}{\sqrt{23}} = 4.46[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 71 - 4.46 = 66.54
The upper end of the interval is the sample mean added to M. So it is 71 + 4.46 = 75.46
The 90% confidence interval for the population mean test score is between 66.54 and 75.46.
