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Answer:
And the upper bound rounded to the nearest integer would be 187.
Step-by-step explanation:
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 mean or variance 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.
The Chi Square distribution is the distribution of the sum of squared standard normal deviates .
represent the sample mean for the sample
population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
Data given: 114 157 203 257 284 299 305 344 378 410 421 450 478 480 512 533 545
The confidence interval for the population variance is given by the following formula:
On this case we need to find the sample standard deviation with the following formula:
And in order to find the sample mean we just need to use this formula:
The sample mean obtained on this case is and the deviation s=132.250
The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:
Since the Confidence is 0.90 or 90%, the value of and
, and we can use excel, a calculator or a tabel to find the critical values.
The excel commands would be: "=CHISQ.INV(0.05,16)" "=CHISQ.INV(0.95,16)". so for this case the critical values are:
And replacing into the formula for the interval we got:
Now we just take square root on both sides of the interval and we got:
And the upper bound rounded to the nearest integer would be 187.