Final answer:
To test population variances' equality for Chemistry and Physics SAT subject tests, calculate the F statistic using sample variances and reference the F-distribution to find the p-value, determining whether to reject the null hypothesis of equal variances.
Step-by-step explanation:
To test the assumption that two population variances are equal using the F-test for equality of variances, you will compare the ratio of the two sample variances. The larger variance is typically placed in the numerator. Given the information for Chemistry (S = 114, n = 15) and Physics (S = 103, n = 15), the F statistic is calculated as (114/103)2. If the F statistic is significantly different from 1, it indicates that the population variances might not be equal.
To find the p-value, reference an F-distribution table or use a calculator with statistical functions, looking at the degrees of freedom corresponding to the two variances (n-1 for both samples).
The approximate p-value is the area under the F-distribution curve beyond the F statistic value. When the p-value is less than the level of significance (commonly 0.05), you reject the null hypothesis that the variances are equal. Without the exact F statistic’s value, we cannot provide the exact p-value, but you would typically use statistical software or a calculator to obtain it.