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Chapter 9: Q 41. (page 581)

Significance tests A test of Ho:p=0.5versus Ha:p>0.5based on

a sample of size 200yields the standardized test statistic z=2.19. Assume that the conditions for performing inference are met.

a. Find and interpret the P-value.

b. What conclusion would you make at the 伪=0.01 significance level? Would

your conclusion change if you used 伪=0.05 instead? Explain your reasoning.

c. Determine the value of p^= the sample proportion of successes.

Short Answer

Expert verified

a. Hypothesis is rejected.

b. 伪=0.01:fail to reject the null hypothesis.and 伪=0.05:reject the null hypothesis

c.p^=0.57774

Step by step solution

01

Part (a) Step 1: Given Information

It is given that z=2.19

n=200

伪=0.5

H0:p=0.5

Ha:p>0.5

02

Part (a) Step 2: Explanation

As z=2.19

P(x<z)=0.98574

P(x>z)=1-0.98574=0.014262

When Pvalue鈮�伪, null hypothesis is rejected.

From above P=0.014262

P=0.014262<伪, null hypothesis is rejected. H0:p=0.5

03

Part (b) Step 1: Given Information

It is given that伪=0.01,伪=0.05

04

Part (b) Step 2: Explanation

Higher the significance level, higher is probability to reject null hypothesis.

As P=0.014262<0.5, so null hypothesis is rejected.

If 伪=0.01P=0.014262>0.01, null hypothesis is not rejected.

If 伪=0.05, P=0.014262>0.05, null hypothesis is not rejected.

Therefore,Pvalue changes with change in significance levels.

05

Part (c) Step 1: Given Information

It is given that n=200

p=0.5

z=2.19

06

Part (c) Step 2: Explanation

We know that z=p^-pp(1-p)n

Hence, 2.19=p^-0.50.5(1-0.5)200

2.19=p^-0.50.5(0.5)200

p^=(2.19脳0.03535)+0.5

Therefore,p^=0.57774

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