A scientist computes a 90% confidence interval to be (4.38,6.02). Using the same

Question

A scientist computes a 90% confidence interval to be (4.38,6.02). Using the same data, she also computes a 95% confindenceinterval to be (4.22, 6.18), and a 99% confidence interval to be(3.91, 6.49). Now she wants to test Ho: = 4 versus H1 : =/ 4. Regarding the P-value, which one of the followingstatements is true? i. P > 0.10 ii. 0.05 < P < 0.10 iii. 0.01 < P < 0.05 iv. P < 0.01 A scientist computes a 90% confidence interval to be (4.38,6.02). Using the same data, she also computes a 95% confindenceinterval to be (4.22, 6.18), and a 99% confidence interval to be(3.91, 6.49). Now she wants to test Ho: = 4 versus H1 : =/ 4. Regarding the P-value, which one of the followingstatements is true? i. P > 0.10 ii. 0.05 < P < 0.10 iii. 0.01 < P < 0.05 iv. P < 0.01

Explanation / Answer

Since both 90% and 95% confidence intervals do not contain = 4, we have to reject H0 at 10% and 5% levels ofsignificance. i.e. P - value < 0.05 But 99% confidence intervals contains = 4,we fail to reject H0 at 1% level of significance. i.e. P - value > 0.01 ==> 0.01 < P - value < 0.05 i.e. P - value > 0.01 ==> 0.01 < P - value < 0.05

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