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The SAT scores the sat subject tests 15 in chem- istry and physics' for two groups of 15 students each electing to take these tests are given below:

Chemistry Physics
X = 644 X = 658
S=114 S = 103
n-15 n=15

To use the two-sample t test with a pooled estimate of o², you must assume that the two population variances are equal. Test this assumption using the F test for equality of variances. What is the approximate p-value for the test?

User Htz
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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.

User Beekeeper
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