Respuesta :
Answer:
The 98% confidence interval for the mean time needed to complete this step is between 52.0403 seconds and 57.1597 seconds
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{1-0.98}{2} = 0.01[/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]1-0.01 = 0.99[/tex], so [tex]z = 2.327[/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 = 2.327\frac{11}{\sqrt{100}} = 2.5597[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 54.6 - 2.5597 = 52.0403 seconds
The upper end of the interval is the sample mean added to M. So it is 54.6 + 2.5597 = 57.1597 seconds
The 98% confidence interval for the mean time needed to complete this step is between 52.0403 seconds and 57.1597 seconds
