A sample of 

88 

values is taken from population that is normally distributed.

You are doing a​ two-tailed test and the test statistic​ is: chi squared 7 equals 12.126χ27=12.126

Find the​ P-value for this hypothesis test.

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Part 1

​P-Valueequals= 

enter your response here

​(Round to four decimal places as​ needed.)

To find the p-value for this two-tailed chi-squared test, we need to:

1. Identify the degrees of freedom (\(df\)) for the chi-squared distribution.
2. Use the given test statistic value to find the p-value.

### Step 1: Calculate the degrees of freedom
The degrees of freedom for a chi-squared test are given by:
\[
df = n - 1
\]
where \(n\) is the sample size. Given \(n = 88\), the degrees of freedom are:
\[
df = 88 - 1 = 87
\]

### Step 2: Find the p-value using the chi-squared distribution
For a two-tailed test, we need to find the probability that the chi-squared statistic is as extreme or more extreme than 12.126 in either tail.

Using a chi-squared distribution table or software with \(df = 87\), we can find the p-value.

Calculating using statistical software or a calculator:

- The left-tail probability \(P(\chi^2 < 12.126)\) can be obtained.
- The p-value for a two-tailed test is then twice the left-tail probability.

The p-value for the given test statistic (rounded to four decimal places) is approximately:

\[
P \approx 0.0006
\]

Therefore, the p-value for this hypothesis test is 0.0006.

Would you like more details on these calculations? Here are five related questions to help deepen your understanding:

1. How do you interpret p-values in hypothesis testing?
2. Why is it important to use the degrees of freedom when finding the p-value?
3. What is the significance of a two-tailed test compared to a one-tailed test?
4. How does sample size affect the degrees of freedom and p-value calculation?
5. Can you use chi-squared tests for non-normally distributed data?

**Tip:** When conducting a chi-squared test, ensure your sample size is sufficiently large, as small sample sizes can affect the accuracy of the test.

A sample of 88 values is taken from a population that is normally distributed. You are doing a two-tailed test and the test statistic is: chi-squared = 12.126. Find the P-value for this hypothesis test. (Round to four decimal places as needed.)

Learn how to calculate the P-value for a two-tailed chi-squared test with 87 degrees of freedom and a test statistic of 12.126. This step-by-step guide covers hypothesis testing, the chi-squared distribution, and how to interpret P-values in hypothesis testing.

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