Consider using a z test to test H0: p = 0.5.
Determine the P-value in each of the following situations. (Round your answers to four decimal places.)
(a) Ha: p > 0.5, z = 1.45
(b) Ha: p < 0.5, z = −2.76
(c) Ha: p ≠ 0.5, z = −2.76
(d) Ha: p < 0.5, z = 0.21
Solution :
Given that,
The null and alternative hypothesis is
H0 : p =0.5
a) Ha: p > 0.5, z = 1.45
This is the right tailed test
Using standard normal table,
P(Z > 1.45)
= 1 - P( Z < 1.45)
= 1 - 0.9265
p-value = 0.0735
b) Ha: p < 0.5, z = −2.76
This is the left tailed test
Using standard normal table,
P( Z < -2.76)
p-value = 0.0029
c) Ha: p ≠ 0.5, z = −2.76
This is the two tailed test
Using standard normal table,
P( Z < -2.76)
= 0.0029
p-value = 2 * P( Z < -2.76)
p-value = 2 * 0.0029
p-value = 0.0058
d) Ha: p < 0.5, z = 0.21
This is the left tailed test
P(Z > 0.21)
= 1 - P( Z < 0.21)
= 1 - 0.5831
p-value = 0.4169
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