Question

3. Five steps of ANOVA Suppose you are interested in how a person's marital status is related to his or her leisure activities. You randomly sample 21 adults and determine the number of hours each person spends per day watching TV or using the Internet for nonwork activities. The data are shown in the following table: Divorced Single Married 5 2 5 mm Nm NNM 4 Conduct an ANOVA test for these data using the five-step computational process.

PLEASE COMPLETE THE FOLLOWING FIVE STEPS OF ANOVA AND FILL IN THE BLANKS. THANKS IN ADVANCE

Answer 1

Step 1

Level of measurement is Nominal.

Populations are normally distributed

Population variances are same.

Step 2

Option B

H₀: The average time spent watching TV or using the Internet is the same, regardless of martial status.

H₁:

Option B

At least one of the population means is different

Step 3

Alpha = 0.01

N = 21

n = 7

Degress of Freedom:

df_Between = a – 1 = 3-1 =2

df_Within = N-a = 21-3 = 18

df_Total = N-1 = 21-1 = 20

F Critical (df_Between, df_Within): (2,18) = 6.01

The degrees of freedom within is dfw = 18

The degrees of freedom between is dfb = 2

F Critical (df_Between, df_Within): (2,18) = 6.01

Step 4

SS_Betwen = ∑(∑a_i)²/n - T²/N = 40.10

SS_Within = ∑(Y)² - ∑(∑a_i)²/n = 26.86

SS_Total = SS_{Betwen ­­}+ SS_Within = 66.95

MS = SS/df

MS_Between = SS_Between/df_Between = 40.10/2 = 20.05

MS_Within = SS_Within/df_Within = 26.86/18 = 1.49

F = MS_effect / MS_error = 20.05/1.49 = 13.44

Hence,

SST = 66.95; SSB = 40.10; SSW = 26.86;

MS_Between = 40.10/2 = 20.05

MS_Within = 26.86/18 = 1.49

F = 13.44

Step 5

Critical = 6.01

Obtained = 13.44

The test statistic falls outside the critical region, so your decision should be to reject the null hypothesis.

Option B

The average time spent watching TV or using the Internet differs significantly by martial status.