Answer:
The 90% confidence interval for the population mean GPA is between 2.53 and 2.89
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].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation(square root of the variance) of the population and n is the size of the sample.
[tex]M = 1.645*\frac{\sqrt{0.25}}{\sqrt{20}} = 0.18[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2.71 - 0.18 = 2.53
The upper end of the interval is the sample mean added to M. So it is 2.71 + 0.18 = 2.89.
The 90% confidence interval for the population mean GPA is between 2.53 and 2.89
