Question

A test of H_{0}: p = 0.5 versus H_{a}: p >
0.5 has the test statistic z = 1.15.

**Part A:** What conclusion can you draw at the 5%
significance level? At the 1% significance level? (6 points)

**Part B:** If the alternative hypothesis is
H_{a}: p ≠ 0.5, what conclusion can you draw at the 5%
significance level? At the 1% significance level?

Answer #1

Solution:

z = 1.15

Part A:

This is a right tailed test.

P-value = P(Z > 1.15 )

= 1 - P(Z < 1.15 )

= 1 - 0.8749

= **0.1251**

**Therefore, P-value = 0.1251 > 0.05, it is concluded
that fail to reject null hypothesis.**

**P-value = 0.1251 > 0.01, it is concluded that fail to
reject null hypothesis.**

Part B :

This is a two tailed hypothesis,

P-value =2* P(Z > 1.15 )

= 2 * (1 - P(Z < 1.15 ))

= 2 * (1 - 0.8749)

= **0.2502**

**Therefore, P-value = 0.2502 > 0.05, it is concluded
that fail to reject null hypothesis.**

**P-value = 0.2502 > 0.01, it is concluded that fail to
reject null hypothesis.**

A test of H0: p = 0.6 versus Ha: p >
0.6 has the test statistic z = 2.27.
Part A: What conclusion can you draw at the 5%
significance level? At the 1% significance level? (6 points)
Part B: If the alternative hypothesis is
Ha: p ≠ 0.6, what conclusion can you draw at the 5%
significance level? At the 1% significance level? (4 points) (10
points)

With H0: p = 0.4, Ha: p < 0.4 , the test statistic is z = –
1.68. Using a 0.05 significance level, the P-value and the
conclusion about null hypothesis are:
ِA) 0.0465; reject H0
B) 0.093; fail to reject H0
C) 0.9535; fail to reject H0
D) 0.0465; fail to reject H0
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B
0.07
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0.871
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0.894
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