This document provides information about two hypothesis tests. For the first test with a t-value of 2.05 and 15 degrees of freedom, the p-value is between 0.025 and 0.05. For the second test with a t-value of -1.84, 15 degrees of freedom and directionality of greater than, the p-value is between 0.90 and 0.95.

1. 1)For the hypothesis test H0 : mean is equal to 10 versus H1 : mean is greater than 10 with
variance unknown and n=15, approximate the P-value for t0 = 2.05. a)0.1 <= p <= 0.05 b)0.01
<= p <= 0.025 c)0.05 <= p <= 0.1 d)0.025 <= p <= 0.05 2) For the hypothesis test H0 : mean is
equal to 10 versus H1 : mean is greater than 10 with variance unknown and n=15, approximate
the P-value for t0 = - 1.84. a)0.80 <= p <= 0.90 b)0.95 <= p <= 0.99 c)0.95 <= p <= 0.975
d)0.90 <= p <= 0.95
Solution
t0=2.05
df=n-1 = 14
look in the t-table for row v=14 for value 2.05
it lies between 1.761 and 2.145 their column alpha are 0.05 and 0.025
so 0.025<=P-value<=0.05