Question

n a survey from 1998, 449 teenagers were surveyed about the music that they listen to. Of these teenagers, 129 of them said that their favorite genre of music is hip-hop. In a similar survey from 2008, 176 of 509 teenagers surveyed said that their favorite genre is hip-hop. Use a two-proportion hypothesis test to determine whether the proportion of teenagers whose favorite genre of music is hip-hop has changed from 1998 to 2008. Assume that the samples are random and independent. Use α=0.01. Let the sample from 1998 correspond to sample 1 and the other to sample 2. (a) Which answer choice shows the correct null and alternative hypotheses for this test?

Answer 1

Answer:

We accept H₀  

Step-by-step explanation:

To compare two proportion:

proportion 1. 1998

n₁  =  449

p₁  =  129/449    p₁  =  0,2873

proportion 2. 2008

n₂  =  509

p₂  =  176/509    p₂  = 0,3457

Test hypothesis

Null Hypothesis                             H₀                 p₂  -  p₁  = 0

Alternative Hypothesis                 Hₐ                 p₂  >  p₁

We have a one tail test ( to the right)

As   α = 0,01 we find in z-table the z score   z = 2,29  ( approximation for 0,011)

To calculate z(s),

z(s) =  ( p₂  -  p₁ ) /√ p*q ( 1/n₁ + 1/n₂)

p = ( x₁ + x₂ ) / n₁ + n₂

p = 129 + 176 / 449 +509

p = 0,3184     and    q =  1  - p       q = 0,6816

1/n₁  + 1/n₂  =  1/ 449  +  1 / 509   =  0,00222 + 0,001964

1/n₁  + 1/n₂  = 0,004184

z(s) =  0,0584/ √(0,3184*0,6816)*0,004184

z(s) =  0,0584/ 0,03013

z(s) = 1,938

z(s) < z(c)        1,938  < 2,29

z(s) is in the acceptance region we accept H₀  at  α = 0,01