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Use the following information to answer the next five exercises. There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?. Write one assumption.

As part of an experiment to see how different types of soil cover would affect slicing tomato production, Marist College students grew tomato plants under different soil cover conditions. Groups of three plants each had one of the following treatments

• bare soil

• a commercial ground cover

• black plastic

• straw

• compost

All plants grew under the same conditions and were the same variety. Students recorded the weight (in grams) of tomatoes produced by each of the $n=15$plants:

Create one-way ANOVA table

The New York Choral Society divides male singers up into four categories from highest voices to lowest: Tenor1, Tenor2, Bass1, Bass2. In the table are heights of the men in the Tenor1 and Bass2 groups. One suspects that taller men will have lower voices, and that the variance of height may go up with the lower voices as well. Do we have good evidence that the variance of the heights of singers in each of these two groups (Tenor1 and Bass2) are different?

Use the following information to answer the next five exercises. There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?. Write another assumption.

Judging by the $F$ statistic, do you think it is likely or unlikely that you will reject the null hypothesis?

What happens to the curves as the degrees of freedom for the numerator and the denominator get larger?

There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?

Write a third assumption

A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. The results are shown in the Table.

$\begin{array}{|lll|}\hline \text{Group A}& \text{Group B}& \text{Group C}\\ 101& 151& 101\\ 108& 149& 109\\ 98& 160& 198\\ 107& 112& 186\\ 111& 126& 160\\ \hline\end{array}$

What is $F$statistic?

A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. The results are shown in the Table.

$\begin{array}{|lll|}\hline \text{Group A}& \text{Group B}& \text{Group C}\\ 101& 151& 101\\ 108& 149& 109\\ 98& 160& 198\\ 107& 112& 186\\ 111& 126& 160\\ \hline\end{array}$

What is$p$-value?

A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. The results are shown in the Table.

$\begin{array}{|lll|}\hline \text{Group A}& \text{Group B}& \text{Group C}\\ 101& 151& 101\\ 108& 149& 109\\ 98& 160& 198\\ 107& 112& 186\\ 111& 126& 160\\ \hline\end{array}$

At the $10\%$significance level, are the scores among the different groups different?