Question

The variance of temperatures in chicken incubators on a chicken farm is generally believed to be 0.5 degrees. The manager of the chicken farm claims that the variance has changed. He randomly tests 25 of his incubators and finds they have a standard deviation of 0.55 degrees. Does this evidence support the manager’s claim that the variance is not 0.5 degrees, at the 0.05 level of significance?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ^2 = 0.5
Alternative Hypothesis, Ha: σ^2 > 0.5

Rejection Region
This is right tailed test, for α = 0.05 and df = 24
Critical value of Χ^2 is 36.415
Hence reject H0 if Χ^2 < 36.415

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (25 - 1)*0.3025/0.5
Χ^2 = 14.52

P-value Approach
P-value = 0.934
As P-value >= 0.05, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the variance is changed from 0.5 degrees