Question

1. An F test with five degrees of freedom in the numerator and seven degrees of freedom in the denominator produced a test statistic whose value was 3.97.

What is the P-value if the test is one-tailed? Round the answer to three decimal places.

2. A hypothesis test is performed, and the P-value is 0.03. State whether the following statements are true or false.

H₀ is rejected at the 5% level.

H₀ is rejected at the 2% level.

H₀ is not rejected at the 10% level.

Answer 1

(1) Using F distribution table, check p value corresponding to the F test statistic(3.97) with df1(5) and df2(7), we get the following p value

(check 5 in the degree of freedom numerator row and check 7 in the degree of freedom denominator column, select the intersecting cell)

p value = 0.050

(2) (A) TRUE, because the p value is less than 0.05 significance level, rejecting the null hypothesis

(B) False because the p value is greater than 0.02 significance level, failed to reject the null hypothesis

(C) False because the p value is less than 0.10 significance level, rejecting the null hypothesis