= Solution
Under the usual <normal linear model> for independent orchard means with common error <variance>, the treatment ratios have null <F-distributions> with denominator six <statistical degrees of freedom>. Their upper-tail <P-values> are approximately
$$
p_S=0.08754,\qquad p_P=0.17798,\qquad p_{SP}=0.47622.
$$
Use the unrounded ratios when evaluating these <P-values>. Thus \b[none of spray, pruning or their <interaction term> is significant at a 5% <significance level>]. Spray gives modest evidence if a 10% <significance level> was chosen in advance, but this is not strong evidence.
\b[Failure to reject does not establish absence of treatment effects.] Only two orchards per combination and six residual <statistical degrees of freedom> leave considerable uncertainty and potentially low <statistical power>. The table alone cannot give the direction or magnitude of individual effects: that requires treatment means. These model-based <F-tests> also rely on appropriate orchard allocation and comparable residual variation; they should not be interpreted as unconditional conclusions from the table alone.
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