Answer:
Step-by-step explanation:
Data given and notation
s represent the sample standard deviation
represent the sample mean
n=23 the sample size
Confidence=95% or 0.95
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 .
Calculating the confidence interval
The confidence interval for the population variance is given by the following formula:
The sample standard deviation for this case was s = 3.8
The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:
Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a tabele to find the critical values.
The excel commands would be: "=CHISQ.INV(0.025,22)" "=CHISQ.INV(0.975,22)". 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: