clarification on null and alternate hypothesis

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Dolphins1544

Guest
#1
I have two questions. I'm pretty sure I have the right answers, but I just wanted clarification on my answers.

1. A university is thinking of adding a +/- to their existing letter grade system if more than 60% of the faculty favor the change. A random sample of 20 faculty was selected. n=the proportion of all faculty that are in favor of adding +/- to the letter grade.
H0: n=0.6 vs. HA: n<0.6
OR
H0: n=0.6 vs. HA: n>0.6

Which pair should they choose??

I said that they should choose the first pair since the alternate hypothesis should always be the opposite of what you want. (I couldn't think of any further reason).

2. A nuclear power plant is not allowed to discharge water warmer than 125 F into the river. They take 50 readings at random times during the month. The hypothesis to be tested are

H0: n=125 vs. HA: n>125. Describe the consequences of type I and type II errors. Which error would you consider to be more serious. Explain.

I said that Type I error would be rejecting that the temp of the water is 125 and say it is greater than 125. Type II error would be that the temp is greater than 125 but we say it is equal to 125. Type II error would then be more serious since we are sending water with temp. greater than 125 into the river and saying it is dqual to 125.



Again, I just want to make sure these are right, and that I don't have them completely switched around!! :) Thanks!
 
#2
I think you're right about the Type I and Type II errors.
In your examples, I would say that null hypotheses should be H0 < or =.60 and H0 < or = 125 (and HA > .60, HA > 125) since they should be 1-way hypotheses.
The HA is what you expect - if you expect that > 60% of faculty want to change the grading system, then your HA is >.60.