Question

ne Sample Hypothesis Tests: Problem 7 Previous Problem List Next (1 point) An article in the Washington Post stated that nearty 45 percent of all Americans take a daily medication. A random sample of n -82 people in Georgia found 30 who take a daily medication. Use this information to test the hypotheses Ho : p = .45 where p represents the population proportion of Georgians who take a daily medication. (a) What is the value of the sample proportion of Georgians who take a daily medication? (b) What is the z test-statistic for this test? (c) What is the p-value of the test? Note: You can earn partial credit on this problem. Preview My Answers Submit Answers Eit

Answer 1

Hypothesis :

$H_a : p \neq 0.45$

Two tailed test.

Given, sample size = n = 82

Number of people who take a daily madication = x = 30

a)

sample proportion = $\hat{p}$ = x/n = 30/82 = 0.36585

b)

z test statistic is given by,

$z = \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$ $= \frac{0.36585 -0.45}{\sqrt{\frac{0.45(1-0.45)}{82}}} = -1.5317$

c )

p-value for this two tailed test is given by,

P-value = 2*P( z < -1.5317 )

Using Excel function ,   =NORMSDIST( z )

P( z < -1.5317 ) = NORMSDIST(-1.5317 ) =0.0628

So , p-value = 2*0.0628 = 0.1256