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.