A researcher studies the effects of fertilizer type (A or B) and soil type (X or Y) on tomato plant height (cm\text{cm}) after 44 weeks, using a balanced design with 33 replicates per combination (n=12n=12 total). A two-way ANOVA is performed at α=0.05α = 0.05. The results are:Based on these results, what is the correct interpretation of the effects of fertilizer type and soil type on plant height?

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Problem 9Multiple Choice

A researcher studies the effects of fertilizer type (A or B) and soil type (X or Y) on tomato plant height ( $cm$ ) after $4$ weeks, using a balanced design with $3$ replicates per combination ( $n equals 12$ total). A two-way ANOVA is performed at $alpha equals 0.05$ . The results are:

Based on these results, what is the correct interpretation of the effects of fertilizer type and soil type on plant height?

There is a significant interaction, so the main effects cannot be interpreted separately

Both fertilizer and soil have significant main effects, with no significant interaction, so their effects are independent

Only soil has a significant main effect

Neither main effect is significant, but there is a significant interaction

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