A state school administrator claims that the standard deviations of science assessment test scores for eighth-grade students are the same in Districts 1 and 2. A sample of 12 test scores from District 1 has a standard deviation of 36.8 points, and a sample of 14 test scores from District 2 has a standard deviation of 32.5 points. At α = 0.10, can you reject the administrator’s claim?

(a) Identify the claim and state H₀ and H_a,

(b) Find the critical value and identify the rejection region,

(c) Find the test statistic F,

(d) Decide whether to reject or fail to reject the null hypothesis,

(e) Interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.