Respuesta :
Answer:
The sample mean used for this interval is 1750.
The sample standard deviation used for this interval was of 175.34
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
The margin of error is the subtraction of these two bounds divided by two.
In this question:
Lower bound: 1690
Upper bound: 1810
Sample mean
[tex]\frac{1690 + 1810}{2} = 1750[/tex]
The sample mean used for this interval is 1750.
Sample standard deviation:
The first step is finding the margin of error:
[tex]M = \frac{1810 - 1690}{2} = 60[/tex]
Now we have to develop the problem a bit.
We want the sample standard deviation, so we use 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 = 25 - 1 = 24
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.711
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
We have that: [tex]M = 60, T = 1.711, n = 25[/tex]
We have to find s
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
[tex]60 = 1.711\frac{s}{\sqrt{25}}[/tex]
[tex]1.711s = 60*5[/tex]
[tex]s = \frac{60*5}{1.711}[/tex]
[tex]s = 175.34[/tex]
The sample standard deviation used for this interval was of 175.34
