Question

Complete a 6-step hypothesis test using the following scenario:

In 2008, a Gallup poll found that 81% of American adults believed that there was a conspiracy theory in the death of President Kennedy. In 2013, the Gallup asked 1039 American adults if they believe there was a conspiracy in the assassination and found that 634 believe there was a conspiracy. Does the data show that the proportion of Americans who believe in this conspiracy has decreased? Test using a 0.10 significance level.

Answer 1

a)

Hypothesis -

H0: p = 0.81

Ha: p < 0.81

b)

Critical value = -1.2816

Rejection region = Reject H0 if test statistics z < -1.2816

c)

Sample proportion = 634 / 1039 = 0.6102

Test statistics

z = - p / sqrt( p( 1 -p ) / n)

= 0.6102 - 0.81 / sqrt( 0.81 * 0.19 / 1039 )

= -16.42

This is test statistics value.

d)

Decision = Since test statistics z falls in rejection region, we have sufficient evidence to reject H0.

e)

p-value = P( Z < z)

= P( Z < -16.42)

= 0

f)

conclusion - We have enough evidence to support the claim that the proportion of Americans who

believe in this conspiracy has decreased.