Sagot :
Answer:
The 95% confidence interval of the population mean total daily travel taxes for Chicago is ($39.13, $41.49).
Step-by-step explanation:
The first step, before building the confidence interval, is finding the mean of the data set.
We are given 200 values, and the with the help of a calculator, the mean of this values is of 40.31.
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].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
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(8.50, as given in the problem) and n is the size of the sample(200).
[tex]M = 1.96\frac{8.50}{\sqrt{200}} = 1.18[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 40.31 - 1.18 = $39.13.
The upper end of the interval is the sample mean added to M. So it is 40.31 + 1.18 = $41.49.
The 95% confidence interval of the population mean total daily travel taxes for Chicago is ($39.13, $41.49).
Answer:
($39.132, $41.488)
A step-by-step explanation is mentioned in the attached image