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Question 4, Instructor-created question
HW Score: $6.67 \%, 1$ of 15 points
Points: 0 of 1
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This is the third problem where we want you to use the $X^{2} c d f$ calculator program to find a p-value when you already have the Test Statistic.

Follow the directions for a TWO tailed test $(\neq)$ for this problem provided on the handout. You will need to actually compare the two standard deviations given in the problem in order to determine if it is a left tail or right tail set-up. If the sample standard deviation, $s$, (the one NOT in the claim) is smaller than the population standard deviation, $\sigma$, the value from the claim, you will use the left tail set-up. But if the sample standard deviation, $s$, is bigger than the population standard deviation, $\sigma$, you will use the right tail set-up. You will need to read carefully. Note, $s$ is always the number you put on the top of the $x^{2}$ formula when you do the test statistic and $\sigma$, the number from the claim, always goes on the bottom.

Use Technology to find the $p$-value for the claim $H 1: \sigma \neq 2.21$, if the test statistic is known to be $X^{2}=27.35$ if $n=31$ and $s=2.11$. Consider the $s$ and $\sigma$. Will this be a left tail or right tail set up?
A. This will be a right-tail set up because $s$ is smaller than $\sigma$
B. This will be a left-tail set up because $s$ is smaller than $\boldsymbol{\sigma}$.

Remember - after using the $x^{2}$ cdf program, since this is a two tail test - you will need to multiply the result you get by TWO before writing down your $p$-value.

What is the p-value? $\square$ Round your answer to 4 decimal places.