I am needing some serious help I am lost I am working on a t

I am needing some serious help. I am lost. I am working on a two-way Anova.

Gender Trailer Type Ratings1-5 Sample Size Mean

Male A 8,7,8,6,4 5 6.6

Make B 4,6,4,5,4 5 4.6

Female A 3,4,1,2,4 5 2.8

Female B 6,7,5,4,7 5 5.8

Now I have to state the hypotheses to test the main effects of gender, the hypotheses to test main effects of trailer type. Calculate the test statistic and p-value for the main effects of gender and trailer type and then state the conclusion of both these tests at the 0.05 level of significance. Please help. I am lost on this

Solution

Now I have to state the hypotheses to test the main effects of gender, the hypotheses to test main effects of trailer type. Calculate the test statistic and p-value for the main effects of gender and trailer type and then state the conclusion of both these tests at the 0.05 level of significance. Please help. I am lost on this

Result 1

Minitab used for analysis.

General Linear Model: score versus Gender, trailer

Method

Factor coding (-1, 0, +1)

Factor Information

Factor   Type   Levels Values

Gender   Fixed       2 Female, Male

trailer Fixed       2 A, B

Analysis of Variance

Source            DF Adj SS Adj MS F-Value P-Value

Gender           1   8.450   8.450     4.83    0.043

trailer          1   1.250   1.250     0.71    0.410

Gender*trailer   1 31.250 31.250    17.86    0.001

Error             16 28.000   1.750

Total             19 68.950

Model Summary

      S    R-sq R-sq(adj) R-sq(pred)

1.32288 59.39%     51.78%      36.55%

Test for interaction,

Test value =17.86, P=0.001 which is less than 0.05.

The interaction is significant.

Test for Gender effect,

Test value =4.83, P=0.043 which is less than 0.05.

The Gender effect is significant.

Test for Trailer effect,

Test value =0.71, P=0.41 which is > than 0.05.

The Trailer effect is not significant.

Result 2

Analysis without interaction

ANOVA: score versus Gender, trailer

Factor   Type   Levels Values

Gender   fixed       2 Female, Male

trailer fixed       2 A, B

Analysis of Variance for score

Source   DF      SS     MS     F      P

Gender    1   8.450 8.450 2.42 0.138

trailer   1   1.250 1.250 0.36 0.557

Error    17 59.250 3.485

Total    19 68.950

S = 1.86689   R-Sq = 14.07%   R-Sq(adj) = 3.96%

Test for Gender effect,

Test value =2.42, P=0.138 which is >than 0.05.

The Gender effect is not significant.

Test for Trailer effect,

Test value =0.36, P=0.557 which is > than 0.05.

The Trailer effect is not significant.

Generally we have to take the result with interaction.