Question

STANDARD VIEW PRINTER VERSIO Chapter 5, Section 1, Exercise 008 The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution 5.1-5.2 Section 003 Section Test Ho : p = 0.27 vs H p <0.27 when the sample has n = 600, and p = 0.219 with SE = 0.02. Find the value of the standardized z-test statistic. 308 ection Round your answer to two decimal places exction action the absolute tolerance is +/-0.01 ction

Answer 1

Answer:

Given that:

The following is a set of hypothesis,some information from one or more samples and a standard error from a randomization distribution

$n=600,\hat{p}=0.219,SE=0.02$

This is the left tailed test .

The null and alternative hypothesis is

Hp <0.27

P=0.219

standard error $SE=[\sqrt {p_0 * (1 - p_0 ) / n}] =0.02$

Test statistic = z

$=\frac{ \hat p - p_0}{[\sqrt{ p_0 * (1 - p_0 ) / n}]}$

$=\frac{ 0.219-0.27 }{[\sqrt{ 0.27 * (1 - 0.27 ) / 600}]}$

$=\frac{ -0.051 }{[\sqrt{ 0.27 * 0.73 / 600}]}$

$=\frac{ -0.051 }{[\sqrt{ 0.1971 / 600}]}$

$=\frac{ -0.051 }{\sqrt{ 0.00032}}$

$=\frac{ -0.051 }{0.0178}$

$=-2.86$

$Z=-2.86$