Question

8.According to the U.S. Census Bureau, 7.1% of Americans living in 2004 were between the ages of 20 and 24. Suppose that a random sample of 400 Americans taken this year yields 35 between the ages of 20 and 24. Test whether the population proportion of Americans aged 20 – 24 is different than the 2004 proportion, using significance level ? = 0.01.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.071

Ha : p 0.071

n = 400

x =35

= x / n = 35 / 400 =0.087

P0 = 0.071

1 - P0 = 1 - 0.071 =0.929

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.087 -0.071 / [(0.071*0.929) / 400 ]

= 1.24

Test statistic = z = 1.24

P(z > 1.24) = 1 - P(z < 1.24 ) = 1 - 0.8925

P-value = 2 * 0.1075 =0.2150

= 0.05

P-value >

0.2150 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that