Question

Some researchers were interested to see how fertilization with nitrogen influenced the yield of canola seed in a set of fields in Canada. They divided the field into 25 blocks to account for a gradient of sun exposure in a randomized block design. The blocks were set up so that each block ran east-west and the different blocks were stacked north-south. They then subdivided each block into a set of sub-blocks for three treatments, no fertilizer, 10 pounds per acre additional fertilizer, or 100 pounds per acre additional fertilizer. Plots were planted with an equivalent density of canola plants (rapeseed, Brassica rapa). The plants were allowed to grow and then harvested so that the yield in pounds of rapeseed per acre could be determined.

Which of the choices below best represents the null hypothesis for this study in the appropriate parameter (e.g. ? or ?)?

The means (µ) of the response for the different levels of the factor are all equal.

The means (µ) of the response for the different levels of the factor are not all equal, (i.e. at least one is different).

The medians (?) of the response for the different levels of the factor are all equal.

The medians (?) of the response for the different levels of the factor are not all equal, (i.e. at least one is different).

The means (µ) of the response for the different levels of the first factor are all equal. The means (µ) of the response for the different levels of the second factor are all equal. There is no interaction between factors.

The means (µ) of the response for the different levels of the first factor are not all equal, (i.e. at least one is different). The means (µ) of the response for the different levels of the second factor are not all equal, (i.e. at least one is different). There is an interaction between factors.

The means (µ) of the response for the different levels of the first factor are all equal. The means (µ) of the response for the different levels of the second factor are all equal (but in some cases we may not be interested in hypothesis testing for this factor).

The means (µ) of the response for the different levels of the first factor are not all equal, (i.e. at least one is different). The means (µ) of the response for the different levels of the second factor are not all equal, (i.e. at least one is different; but in some cases we may not be interested in hypothesis testing for this factor).

Which of the choices below best represents the alternative hypothesis for this study in the appropriate parameter (e.g. ? or ?)?

The means (µ) of the response for the different levels of the factor are all equal.

The means (µ) of the response for the different levels of the factor are not all equal, (i.e. at least one is different).

The medians (?) of the response for the different levels of the factor are all equal.

The medians (?) of the response for the different levels of the factor are not all equal, (i.e. at least one is different).

The means (µ) of the response for the different levels of the first factor are all equal. The means (µ) of the response for the different levels of the second factor are all equal. There is no interaction between factors.

The means (µ) of the response for the different levels of the first factor are not all equal, (i.e. at least one is different). The means (µ) of the response for the different levels of the second factor are not all equal, (i.e. at least one is different). There is an interaction between factors.

The means (µ) of the response for the different levels of the first factor are all equal. The means (µ) of the response for the different levels of the second factor are all equal (but in some cases we may not be interested in hypothesis testing for this factor).

The means (µ) of the response for the different levels of the first factor are not all equal, (i.e. at least one is different). The means (µ) of the response for the different levels of the second factor are not all equal, (i.e. at least one is different; but in some cases we may not be interested in hypothesis testing for this factor)

What should the alpha (?) value be for this study?

Based on these data, the best choice of a statistical test to address this question is:

A one-way analysis of variance.

The Kruskal-Wallis test.

A two-way analysis of variance with interactions for factorial experiments.

A two-way analysis of variance without interactions for a randomized block design.

A two-way analysis of variance with repeated measures.

None of the other choices is appropriate.

Answer 1

The null hypothesis is - The means (µ) of the response for the different levels of the first factor are not all equal, (i.e. at least one is different).

The means (µ) of the response for the different levels of the second factor are not all equal, (i.e. at least one is different).

There is an interaction between factors.

The alternative hypothesis is - The means (µ) of the response for the different levels of the first factor are not all equal, (i.e. at least one is different).

The means (µ) of the response for the different levels of the second factor are not all equal, (i.e. at least one is different).

There is an interaction between factors.

What should the alpha (?) value be for this study? = 0.05

Based on these data, the best choice of a statistical test to address this question is:

A two-way analysis of variance with interactions for factorial experiments.