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- Chapter 12 - T/F

Shan A.

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The *F* distribution's curve is positively skewed.

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The test statistic used in ANOVA is *Student's t*.

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There is one, unique *F* distribution for a F-statistic with 29 degrees of freedom in the numerator and 28 degrees of freedom in the denominator.

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One characteristic of the *F* distribution is that *F* cannot be negative.

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One characteristic of the *F* distribution is that the computed *F* can only range between -1 and +1.

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The shape of the *F* distribution is determined by the degrees of freedom for the *F-*statistic, one for the numerator and one for the denominator.

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Like Student's *t* distribution, a change in the degrees of freedom causes a change in the shape of the F distribution.

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If the computed value of *F* is 0.99 and the critical value is 3.89, we would not reject the null hypothesis.

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For the hypothesis test, Ho:o1=o2, with n_{1} = 10 and n_{2} = 10, the F-test statistic is 2.56. At the 0.01 level of significance, we would reject the null hypothesis.

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For the hypothesis test, Ho:o1=o2, with n_{1} = 4 and n_{2} = 4, the F-test statistic is 50.01. At the 0.01 level of significance, we would reject the null hypothesis.

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False

For the hypothesis test, Ho:o1=o2, with n_{1} = 7 and n_{2} = 7, the F-test statistic is 2.56. At the 0.05 level of significance, we would reject the null hypothesis.

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True

For the hypothesis test, Ho:o1=o2, with n_{1} = 9 and n_{2} = 9, the F-test statistic is 4.53. At the 0.05 level of significance, we would reject the null hypothesis.

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To employ ANOVA, the populations being studied must be approximately normally distributed.

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To employ ANOVA, the populations should have approximately equal standard deviations.

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In an ANOVA table, *k* represents the total number of sample observations and *n* represents the total number of treatments.

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False

The alternate hypothesis used in ANOVA is u1=u2=u3*. *

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The alternate hypothesis for ANOVA states that not all the means are equal.

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For an ANOVA test, rejection of the null hypothesis does not identify which treatment means differ significantly.

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If the computed value of *F* is 4.01 and the critical value is 2.67, we would conclude that all the population means are equal.

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If we want to determine which treatment means differ, we compute a confidence interval for the difference between each pair of means.

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If a confidence interval for the difference between a pair of treatment means includes 0, then we fail to reject the null hypothesis that there is no difference in the pair of treatment means.

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If the endpoints of a confidence interval for the difference between a pair of treatment means are both positive numbers, then we reject the null hypothesis that there is no difference in the pair of treatment means.

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A treatment is a specific source of variation in a set of data.

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A blocking effect is a specific source of variation in a set of data.

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When a blocking effect is included in an ANOVA, the result is a smaller error sum of squares.

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When a blocking effect is included in an ANOVA, two sources of variation are reported: treatment variation and block variation.

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When a blocking effect is included in an ANOVA, the analysis is more likely to detect differences in the treatment means.

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The F-statistic to test for a blocking effect is computed as the ratio of the Treatment Mean Square and the Block Mean Square.

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In a two-way ANOVA, the sum of the treatment, block, and error degrees of freedom equal the total degrees of freedom.

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False

In a two-way ANOVA, the sum of the treatment and block mean squares equals the error mean square.

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In a two-way ANOVA, the sum of the treatment, block, and error sum of squares equals the total sum of squares.

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In a two-way ANOVA with interaction, there are two factor effects and an interaction effect.

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In an interaction plot, parallel lines are an indication that there is no interaction effect.

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Interaction between two factors occurs when the effect of one factor on the response variable is the same for any value of another factor.

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