Respuesta :
Answer:
The sample mean is of 1925 calories.
The margin of error is of 75 calories.
The sample standard deviation is of 109.7992 calories.
Step-by-step explanation:
Sample mean:
The sample mean is the mean value of the two bounds of the confidence interval. So
[tex]M = \frac{1850 + 2000}{2} = 1925[/tex]
The sample mean is of 1925 calories.
The margin of error
Difference between the bounds and the sample mean. So
2000 - 1925 = 1925 - 1850 = 75 calories.
The margin of error is of 75 calories.
Sample standard deviation:
Here, I am going to expand on the t-distribution.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 18 - 1 = 17
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.898
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
Since [tex]M = 75, T = 2.898, n = 18[/tex]
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
[tex]75 = 2.898\frac{s}{\sqrt{18}}[/tex]
[tex]s = \frac{75\sqrt{18}}{2.898}[/tex]
[tex]s = 109.7992[/tex]
The sample standard deviation is of 109.7992 calories.
