Question

According to the Nielsen Media Research, children (ages 2–11) spend an average of 21 hours 30 minutes watching television per week while teens (ages 12–17) spend an average of 20 hours 40 minutes. Based on the sample statistics obtained below, is there sufficient evidence to conclude a difference in average television watching times between the two groups? Use α = 0.01 Children Teens

Sample mean 22.45 18.50

Sample variance 16.4 18.2

Sample size 15 15

Answer 1

Given :

α = 0.01

For children

Sample mean= 22.45

Sample variance =16.4

Sample size=N1= 15

For Teens

Sample mean =18.50

Sample variance =18.2

Sample size N2=15

We have to find the population variance that are found by the given formula

$Sp\ = \sqrt{\frac{\ (N1 -1 ) \ * Sample\ varience \ of \ children\ + \ (N2\ -1 )\ * Sample\ varience \ of \ teens}{N1\ + N2\ - \ 2} }$

On putting the value in the given formula we will get

$\sqrt{17.3}$

=4.1593

Now we have test the hypothesis that can be determined by the given formula

$H_{O}=\ U1-U2 =0\\H_{A}=\ U1-U2 \neq 0$

Test the condition by using the given formula

$t1\ = \frac{Sample\ mean\ of\ children - Sample\ mean \ of \ teen}{sp\sqrt{\frac{1}{N1} + \frac{1}{N2} } }$

On putting the value we will get 2.60

Now the p value can be determined by the degree of freedom that is

p=0.0167

p>α

We will never reject the null hypothesis.

Therefore There is no sufficient evidence to conclude a difference in average television