Question

In a random sample of 200 adults and 300 teens who watched a certain television show, 50 adults and 150 teens said they liked the show. prove with a 5% significance that the difference between the proportion of adults and adolescents who watch the program is equal to 0.10

Answer 1

For adults

n1 = 200, x1= 50,   = 0.25

For teens

n2 = 300, x2= 150,   = 0.5

Here our null hypothesis is, Ho: p1-p2=0.10

Alternate hypothesis HA: p1-p2 0.10

Test statistic=

Where , = = = 0.4

So, The test statistic is = = -7.83

Critical value, Z(0.05.2)=

As the test statistic < Critical value;

Now the test statistic lie in the critical region that means that we will reject the null hypothesis.

Hence we donot have enough evidence to support the claim that the diffrence between the proportion of adults and teens who watch the show is 0.1