Answer:
The p-value is between .025 and .05
p-value = 0.028
The critical region is χ² ≥ 24.996
Using both approaches the decision is to reject the null hypothesis.
Step-by-step explanation:
Hello!
You have the following hypothesis
H₀: σ² ≤ 50
H₁: σ² > 50
α: 0.05
To test the population variance, the statistic to use has is Chi-Square distribution:
χ²=<u> (n-1)S² </u> ~χ²
σ²
With n= 16 and S= 9.5
The statistic value is:
χ²=<u> (16-1)(9.5)² </u> = 27.075
50²
This is a one-tailed test, to calculate the p-value you have to calculate the probability of the χ² value.
P(χ² ≥ 27.075) = 1 - P(χ²
< 27.075) = 1 - 0.972 = 0.028
The p-value is between .025 and .05
p-value = 0.028
Since the p-value ≤ α the decision is to reject the null hypothesis. You can conclude that the population variance is greater than 50.
As I said this is a one-tailed test, the critical value is:
χ² = χ²
= 24.996
Decision:
If χ² ≥ 24.996 then you reject the null hypothesis.
If χ² < 24.996 then you support the null hypothesis.
Since the calculated χ² value is greater than the critical value, you reject the null hypothesis.
I hope you have a SUPER day!