Question

Consider using a z test to test Ho: P = 0.6. Determine the P-value in each of the following situations. (Round your answers to four decimal places.) (a) Ha:p> 0.6, z = 1.46 (b) H:P < 0,6, z = -2.71 (c) H: P = 0.6, z = -2.71 (d) HP < 0.6, z = 0.24

Answer 1

Solution :

a) The null and alternative hypothesis are

H₀ : $\mu$ = 0.6   ........... Null hypothesis

H_a: $\mu$ > 0.6 ........... Alternative hypothesis

Given, z = 1.46

> sign in Ha indicates that the test is ONE TAILED.

z = 1.46

So , using calculator ,

p-value = P(z > 1.46)

= 0.0721

p value = 0.0721

b)  The null and alternative hypothesis are

H₀ : $\mu$ = 0.6   ........... Null hypothesis

H_a: $\mu$ < 0.6 ........... Alternative hypothesis

Given, z = -2.71

< sign in Ha indicates that the test is ONE TAILED.

z = -2.71

So , using calculator ,

p-value = P(z < -2.71)

= 0.0034

p value = 0.0034

c)  The null and alternative hypothesis are

H₀ : $\mu$   = 0.6   ........... Null hypothesis

H_a: $\mu$ $\neq$ 0.6 ........... Alternative hypothesis

Given, z = -2.71

$\neq$ sign in Ha indicates that the test is TWO TAILED.

z = -2.71

So , using calculator ,

p-value = P(z < -2.71) + P(z > 2.71)

= 0.0034 + 0.0034

p value = 0.0068

d)  The null and alternative hypothesis are

H₀ : $\mu$ = 0.6   ........... Null hypothesis

H_a: $\mu$ < 0.6 ........... Alternative hypothesis

Given, z = 0.24

< sign in Ha indicates that the test is ONE TAILED.

z = 0.24

So , using calculator ,

p-value = P(z < 0.24)

= 0.5948

p value = 0.5948