Question

Heat can denature proteins causing them to cease to function, and this can impact various metabolic rates in organisms. However, many organisms have mechanism to tolerate short periods of high temperature. To determine if tobacco plants can effectively tolerate short periods of high temperature and see how quickly they recover scientists measured the photosynthetic rates (in µmol of CO2 consumed per minute per gram) of 5 tobacco plants one day before (time 0), one day after (time 1), and one week after (time 2) being exposed to temperatures of 120°F for two hours. The researchers wanted to know if rates of photosynthesis were altered at the different times. The researchers were also not interested in testing hypotheses about differences among the 5 plants they used for the study.

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.