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I'm reviewing for my final exam and this question was asked: (help with formatting please, I'm new)

Problem

The logic all makes sense to me, but their conclusions in part e and f are either wrong or really confusing me.

For example, in part e, given that the null hypothesis is a "less than or equal to" one, that means that the test should be one-sided, correct? So if the cdf of the function is more than 0.95, the null hypothesis should be rejected (since alpha = 0.05). But their answer says that it must be greater than 0.975? My only logic behind this is if they accidentally believed alpha to be 0.025 or divided alpha by 2 as if it were a two-tailed test? This isn't making sense to me, but correct me if I'm wrong

A similar situation happens in part e, as when I plug into my calculator for the tcdf(low=2,max=1E99,df=25), I get 0.02823. But their p-value is 0.05, as if they got double my answer?

I've frequently referenced tables and my calculator for any solution but I keep finding out that my answer is right. My professor rarely makes mistakes and he's unavailable for questioning. Any help or sanity check would be great!

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