​(c) Find the standardized test statistic for the 

chiχsquared2​-test.

chiχsquared2equals=enter your response here 

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

To find the standardized test statistic for the chi-square test, we use the formula:

\[
\chi^2 = \frac{(n - 1)s^2}{\sigma_0^2}
\]

Where:
- \(n = 12\) (sample size)
- \(s = 0.001975\) (sample standard deviation)
- \(\sigma_0 = 0.005\) (hypothesized population standard deviation)

Now, we will compute the test statistic.The standardized test statistic for the chi-square test is approximately \(\chi^2 = 1.717\).

Would you like to proceed with the hypothesis decision based on this test statistic, or do you have any other questions? 

### Relative Questions
1. What is the significance level (\(\alpha\)) and how is it chosen?
2. How does the chi-square distribution differ from the normal distribution?
3. What are the assumptions required for the chi-square test to be valid?
4. How is the sample variance different from the population variance?
5. What does it mean to have a two-tailed test?
6. How do we interpret the result if the test statistic falls within the critical region?
7. Can the chi-square test be used for non-normal distributions?
8. What are the consequences of a Type I error in this context?

### Tip
When performing hypothesis testing, always check if the assumptions (e.g., normality of data, random sampling) are met to ensure the validity of the results.

Learn how to calculate the standardized test statistic for the chi-square test with a step-by-step explanation. This problem involves statistics and hypothesis testing, focusing on the chi-square test statistic formula and its application. Suitable for advanced college-level students and researchers.

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