Question

Video games In a poll of 1,063 randomly selected adult gamers conducted by the Pew Internet Project, 54% of the adult gamers interviewed reported that they used a gaming console (such as an Xbox 360, PS3 or Wii) to play video games. In a separate Pew study, 89% of 1,064 randomly selected teen gamers reported that they used a gaming console. Perform a hypothesis test to evaluate the claim that teen gamers are more likely to use a gaming console than adult gamers.

Answer 1

Solution:

Given:

Teen gamers:

n₁ = 1064

Adult gamers:

n₂ = 1063

Claim: Teen gamers are more likely to use a gaming console than adult gamers.

Step 1) State H0 and H1:

H₀: p₁ = p₂ Vs H₁: p₁ > p₂ ( Right tailed test)

Step 2) Find test statistic value:

where

Thus

Step 3) Critical value:

Level of significance =

Since this is right tailed test, Find Area = 1 - 0.05 = 0.95

Look in z table for Area = 0.9500 or its closest area and find corresponding z value.

Area 0.9500 is in between 0.9495 and 0.9505 and both the area are at same distance from 0.9500

Thus we look for both area and find both z values

Thus Area 0.9495 corresponds to 1.64 and 0.9505 corresponds to 1.65

Thus average of both z values is : ( 1.64+1.65) / 2 = 1.645

Thus Z_critical = 1.645

Step 4)  Decision Rule:
Reject null hypothesis ,if z  test statistic value > z critical value = 1.645, otherwise we fail to reject H0.

Since   z  test statistic value = > z critical value = 1.645, we reject null hypothesis H0.

Step 5) Conclusion:

At 0.05 level of significance, we have sufficient evidence to support the claim that: teen gamers are more likely to use a gaming console than adult gamers.