Use a x squared-test to test the claim about the population variance or standard deviation at the given level of significance and using the given sample statistics.
Claim: ơ2 ≤ 60; α = 0.025. Sample statistics: s2 = 72.7, n = 15
Is x-squared supposed to mesoan chi-squared?
I think so, yes. I did not know how to type the symbols correctly on computer.
To test the claim about the population variance or standard deviation, we can use a Chi-squared test. The null hypothesis (H₀) assumes that the population variance (σ²) is less than or equal to the claimed value (60), while the alternative hypothesis (H₁) assumes that the population variance is greater than the claimed value.
To perform the Chi-squared test, we need to calculate the test statistic and compare it to the critical value from the chi-squared distribution with appropriate degrees of freedom at the given level of significance.
Step 1: State the null and alternative hypothesis:
H₀: σ² ≤ 60
H₁: σ² > 60
Step 2: Determine the level of significance (α):
Given α = 0.025
Step 3: Calculate the test statistic:
The test statistic for the Chi-squared test for population variance is given by:
χ² = (n - 1) * s² / σ²
Given sample statistics:
s² = 72.7
n = 15
Plugging in the values:
χ² = (15 - 1) * 72.7 / 60
Step 4: Determine the critical value:
The critical value is the value from the chi-squared distribution with (n - 1) degrees of freedom at the given level of significance. In this case, the degrees of freedom is (n - 1) = (15 - 1) = 14. Using a table or statistical software, we can find the critical value associated with α = 0.025 and 14 degrees of freedom.
Step 5: Compare the test statistic to the critical value:
If the test statistic is greater than the critical value, we reject the null hypothesis in favor of the alternative hypothesis. Otherwise, we fail to reject the null hypothesis.
If χ² > critical value, we reject H₀
If χ² ≤ critical value, we fail to reject H₀
By comparing the calculated test statistic (χ²) to the critical value, we can determine whether or not to reject the null hypothesis and make conclusions about the claim regarding the population variance or standard deviation.