We can rewrite the expression under the radical as
then taking the fourth root, we get
Why the absolute value? It's for the same reason that
since both and
return the same number
, and
captures both possibilities. From here, we have
The absolute values disappear on all but the term because all of
,
and
are positive, while
could potentially be negative. So we end up with
Answer:
a) The 99% confidence interval would be given by (5004.168;12603.832)
b) For this case we can use the lower bound for the confidence interval as estimation, on this case 5004.168. But we need to take in count that this value it's with 99% of confidence and 1% of significance and 1% of probability to commit type Error I
Step-by-step explanation:
1) Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
s=5629 represent the sample standard deviation
n=20 represent the sample size
2) Part a
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.99 or 99%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,19)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 99% confidence interval would be given by (5004.168;12603.832)
3) Part b
For this case we can use the lower bound for the confidence interval as estimation, on this case 5004.168. But we need to take in count that this value it's with 99% of confidence and 1% of significance and 1% of probability to commit type Error I
Answer:
LQ = 54
Median = 69
UQ = 94
Step-by-step explanation:
This list is already sorted for you, so you don't need to worry about that, otherwise you would need to sort the numbers in ascending order. To find the median, we do , where n is the amount of numbers. This gives us 4, so the median is at position 4, so the median is 69. The lower quartile is simply
, so 2, so the lower quartile is 54. The upper quartile is
, so 6, so the upper quartile is 94.