## A sample standard deviation of 10 weights of packages of grass seed distributed by a certain company was calculated to be 0.286. Assume that

Question

A sample standard deviation of 10 weights of packages of grass seed distributed by a certain company was calculated to be 0.286. Assume that weights are normally distributed and find a 95% confidence interval for the standard deviation of all such packages of grass seed

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2021-09-13T15:36:11+00:00
2021-09-13T15:36:11+00:00 1 Answer
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## Answers ( )

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

Step-by-step explanation:Data given and notation

s=0.286 represent the sample standard deviation

represent the sample mean

n=10 the sample size

Confidence=95% or 0.95

A

confidence intervalis “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 erroris the range of values below and above the sample statistic in a confidence interval.The

Chi Square distributionis 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 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 table to find the critical values.

The excel commands would be: “=CHISQ.INV(0.025,9)” “=CHISQ.INV(0.975,9)”. 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: