Question

Problem 3. Hours of TV watched per week for a random sample of men and women from each of three age groups are collected and reported in the following table. 18-24 Age Group 25-54 55+ Male Female A) What is the most suitable statistical design to analyze this data (1 pt) B) Identify all the factor(s) and level(s) of each factors (2 pts) I summarized the data for you and obtained the following (partial ???) results. SSTOT=2412.70; SS(gender)= 353.63; SS(Age)=1,520; SSE=429.70. D. Complete the ANOVA Table and test all the null hypotheses you identified above and state your conclusions. (7 pts)

Answer 1

A)

As we can clearly see that two way effects are given in the above table. so we will apply two way anova design to analyse this data.

B)

AS we can see that their are 3 levels of age group and 2 factors (male and female)

C & D)

Here ANOVA table is given by:

Source	df	SS	MS	F
Gender	1	353.63	353.63	21.3972074
Age	2	1520	760	45.9855713
Error	26	429.7	16.5269231
Total	29	2412.7

Here SS(Sum of squares) is already given. we just need to find the MS which is nothing but SS/df with respect to each row

like for Age their are 3 age groups given. SO df = 3-1 = 2

ans MSage = SSage/df = SSage/2 = 1520/2 = 760

And then F statistic is given by = MSage/MSE =

Similarly we can find for Gender.

SO

F statistic for Gender will follow F distribution with (1, 26) df

and similarly F statistic for Age will follow F distribution with (2, 26) df

So now we can find the critrical value at for both of them in R

90'0 = 0

> qf(.95, 1, 26)

[1] 4.225201

> qf(.95, 2, 26)

[1] 3.369016

Here is the code

Now For Age

F = 45.9855713 > F_critical = 3.369016

which implies that we have enough evidence to reject H0

i.e., here Age has significant role in hours of TV watching.

Similarly for Gender

F = 21.3972074 > F_critical = 4.225201

which implies that we have enough evidence to reject H0

i.e., here Gender  has also significant role in hours of TV watching.