Respuesta :
Answer:
a) The 95% confidence interval estimate for average daily sales is between $135,080 and $142,920.
b) The 97% confidence interval estimate for average daily sales is between $134,660 and $143,340.
Step-by-step explanation:
a) provide a 95% confidence interval estimate for average daily sales.
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{12000}{36} = 3920[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 139000 - 3920 = $135,080
The upper end of the interval is the sample mean added to M. So it is 139000 + 3920 = $142,920
The 95% confidence interval estimate for average daily sales is between $135,080 and $142,920.
b) provide a 97% confidence interval estimate for average daily sales.
By the same logic as above, now Z = 2.17.
[tex]M = 2.17*\frac{12000}{36} = 4340[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 139000 - 4340 = $134,660
The upper end of the interval is the sample mean added to M. So it is 139000 + 4340 = $143,340
The 97% confidence interval estimate for average daily sales is between $134,660 and $143,340.
