A survey with 49 persons was conducted to analyze the
design of an advertising campaign. Each respondent was asked to
evaluate the overall impression of the advertisement on an
eleven-point scale from 0 (bad) to 10 (good). The evaluations are
summarized separately with respect to type of occupation of the
respondents in the following figure.
To analyze the influence of occupation on the evaluation of the
advertisement an analysis of variance was performed:
Res.Df RSS Df Sum of Sq F Pr(>F)
1 48 24.789
2 45 24.642 3 0.147 0.089 0.96565
Which of the following statements are correct?
A one-sided alternative was tested for the mean values.
It can be shown that the evaluation of the respondents depends on their occupation. (Significance level
The fraction of explained variance is larger than
The fraction of explained variance is smaller than
The test statistic is smaller than
In order to be able to answer the questions the fraction of
explained variance has to be determined. The residual sum of squares
when using only a single overall mean value (
well as the residual sum of squares when allowing different mean
values given occupation (
) are required. Both are
given in the RSS column of the ANOVA table. The
fraction of explained variance is given by
The statements above can now be evaluated as right or wrong.
False. An ANOVA always tests the null hypothesis, that all mean values are equal against the alternative hypothesis that they are different.
and hence not significant. It can not be shown that the evaluations differ with respect to the occupation of the respondents.
False. The fraction of explained variance is
and hence not larger than 0.59.
True. The fraction of explained variance is
and hence smaller than 0.56.
True. The test statistic is
and hence smaller than