Question

Let μ denote the mean reaction time to a certain stimulus. For a large-sample z test of H₀: μ = 5 versus H_a: μ > 5, find the P-value associated with each of the given values of the z test statistic. (Round your answers to four decimal places.)

(a)    1.38
(b)    0.92
(c)    1.88
(d)    2.44
(e)    −0.26

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H0 :    = 5

Ha : > 5

a ) Test statistic = z =1.38

P(z > 1.38 ) = 1 - P(z < 1.38 ) = 1 - 0.9162

P-value = 0.0838

b ) Test statistic = z = 0.92

P(z >  0.92 ) = 1 - P(z <  0.92 ) = 1 - 0.8212

P-value = 0.1788

c ) Test statistic = z = 1.88

P(z >  1.88 ) = 1 - P(z <  1.88 ) = 1 - 0.9699

P-value = 0.0301

d ) Test statistic = z = 2.44

P(z > 2.44 ) = 1 - P(z < 2.44 ) = 1 - 0.9927

P-value = 0.0073

e ) Test statistic = z =−0.26

P(z > −0.26 ) = 1 - P(z < −0.26 ) = 1 - 0.3974

P-value = 0.6026