Respuesta :
Answer:
The 95% confidence limits for the population mean listening time are 105.84 minutes and 114.16 minutes.
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{1-0.95}{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{30}{\sqrt{200}} = 4.16[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 110 - 4.16 = 105.84 minutes.
The upper end of the interval is the sample mean added to M. So it is 110 + 4.16 = 114.16 minutes.
The 95% confidence limits for the population mean listening time are 105.84 minutes and 114.16 minutes.
