Question

40. Suppose a researcher wants to test the hypothesis that µ = 25 versus the alternative that µ ≠ 25 using data from a random sample of 95 people.  We calculate the standardized test statistic to be 2.087.  Which of the following best describes the p-value?

	a.	0.02 < p-value < 0.04
	b.	0.04 < p-value < 0.05
	c.	0.01 < p-value < 0.02
	d.	0.05 < p-value < 0.04
	e.	0.02 < p-value < 0.025

Answer 1

Solution :

This is the two tailed test,  

The null and alternative hypothesis is ,

H0 :   = 25

Ha :    25

degrees of freedom = n - 1 = 95 - 1 = 94

Test statistic = t = 2.087

P( t > 2.087 ) = 1 - P( t < 2.087 ) = 1 - 0.9802 = 0.02

P-value = 2 * P( t > 2.087 )

P-value = 2 * 0.02

P-value = 0.04

b.	0.04 < p-value < 0.05