Question

In April​ 2010, 46​% of the unemployed had been out of work longer than six months. Policy makers felt that this percentage declined during 2010 as the job market improved. To test this​ theory, a random sample of 200 unemployed people was​ selected, and it was found that 82 had been out of work for more than six months. Using a level of significance level of 0.10

A. Determine the critical values of the test statistic

(round to two decimal places)

B. p-value=

(round to three decimal places)

Answer 1

Solution:

Claim:percentage declined during 2010 as the job market improved

H₀: p = 0.46

H_a: p < 0.46

A)

Left tailed test

Given level of significance level of 0.10

For left tailed test , critical value is

Answer : critical value is -1.28

B)

Let   be the sample proportion.

= x/n = 82/200 = 0.41

The test statistic z is

z =

=  (0.41- 0.46)/[0.46*(1 - 0.46)/200]

= -1.42

Now ,

for left tailed test , p value = P(Z < -1.42) = 0.078

p value = 0.078