Question

Limpets are small snail-like mollusks that have more or less conical (rather than coiled) shells. Many species of limpets can exist in saltwater but may also move into brackish water (less salty than seawater, but still not quite freshwater). A researcher was interested to see if existing in water with different salt concentrations altered the rate at which two species of limpets (Acmaea scabra and Acmaea digitalis) consumed oxygen (measured in µL of O2/mg of dry body weight/minute). The salt concentrations were 1.00 = 100% seawater, 0.75 = 75% seawater, and 0.50 = 50% seawater. It is also possible that the species could respond differently to salinity, so the factors could interact. For the purposes of this study seawater is 1 and species is 2.

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 factor are all equal.

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

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.