Question

In testing H0:μ=77 versus Ha:μ≠77 for some population, a random sample of 17 observations from a normally distributed population with unknown standard deviation yielded a test statistic of 2.638.   The  p-value for this test is

Select one:

a. 0.0041

b. between 0.005 and 0.010

c. between 0.01 and 0.02

d. 0.0082

e. impossible to determine based on the given information.

Answer 1

Solution :

The null and alternative hypothesis is ,

H0 :   = 77

Ha :    77

This is the two tailed test,

Test statistic = t = 2.638

n = 17

degrees of freedom = n - 1 = 17 - 1 = 16

P(t > 2.638) = 1-P (t < 2.638) = 1 - 0.9910 = 0.0090

P-value = 2 * P(t > 2.638)

P-value = 2 * 0.0090

P-value = 0.0180

c. between 0.01 and 0.02