SOLUTION: I am always confused in hypothesis questions.I tried solving the question but I don't understand that what this question is asking. Consider the hypothesis test where the hypoth

Question 1129683: I am always confused in hypothesis questions.I tried solving the question but I don't understand that what this question is asking.
Consider the hypothesis test where the hypotheses are Ho: � = 26.4 and Ha: � < 26.4. A sample of size 64 is randomly selected and yields a sample mean of 23.6.
If it is known that σ = 12, how many standard errors below � = 26.4 is the sample mean, �x=23.6?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
It's better to write the hypotheses as including everything. If Ha is mu < 26.4, then Ho is mu >=26.4
alpha is usually 0.05 (not always)
test statistic is a z
critical value is z<-1.645
calculation is z< (x bar-mean)/sigma/sqrt(n)
In any case the SE is sigma/sqrt(n) or 12/sqrt(64)=1.5
So 23.6 is 0.8 below 26.4, and that would be .8/1.5 or 0.53 SE below 26.4
This would be a z-test, and a value of z <=-0.53 is going to be larger than most levels of significance (nearly 30%)
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