Answer:
a)
b)
Rounded to the nearest number would be:
c)
And rounded :
Step-by-step explanation:
Data given and notation
s=30 represent the sample standard deviation
represent the sample mean
n=20 the sample size
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 .
Part a
The best point of estimate for the population variance is the sample variance, so on this case:
Part b
The confidence interval for the population variance is given by the following formula:
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 table to find the critical values.
The excel commands would be: "=CHISQ.INV(0.05,19)" "=CHISQ.INV(0.95,19)". so for this case the critical values are:
And replacing into the formula for the interval we got:
Rounded to the nearest number would be:
Part c
In order to find the confidence interval for the deviation we just need to take the square root for the interval of the variance, and we got:
And rounded :