Use technology to construct the confidence intervals for the population variance sigma σ squared 2 and the population standard deviation sigma σ. Assume the sample is taken from a normally distributed population. c equals = 0.90 0.90, s equals = 31 31, n equals = 17 17 The confidence interval for the population variance is ( 26.30 26.30, 7.96 7.96). (Round to two decimal places as needed.) Enter your answer in the edit fields and then.

Now we just take square root on both sides of the interval and we got:

Step-by-step explanation:

Data given and notation

s=31 represent the sample standard deviation

represent the sample mean

n=17 the sample size

Confidence=90% or 0.90

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 deviation for this case is s=31

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(0.05,16)" "=CHISQ.INV(1-0.05,7)". 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:

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