SOLUTION: assuming that my null hypothesis is that males and females are equally likely to sign up for a stats course, my alternate hypothesis is that the probability of males signing up is

Question 399141: assuming that my null hypothesis is that males and females are equally likely to sign up for a stats course, my alternate hypothesis is that the probability of males signing up is 0.3, alpha is set at 0.05 and n is 25. i need to find the critical value of y as well as beta, how do i do this i am so stuck?
Found 2 solutions by stanbon, robertb:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Assuming that my null hypothesis is that males and females are equally likely to sign up for a stats course, my alternate hypothesis is that the probability of males signing up is 0.3, alpha is set at 0.05 and n is 25. i need to find the critical value of y as well as beta, how do i do this i am so stuck?
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Well, that's a bit confusing.
If Ho is p(m)-p(f) = 0
then Ha should be p(m)-p(f) is not 0
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It appears that a sample 25 people was taken and 30% of them were males.
Based on alpha being 5% and the fact that you are doing a 2-tail test,
the critical values are z = +-1.96.
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Cheers,
Stan H.
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Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
: or ()
:
Since n = 25 it is small-sampling, and you have to use the t-test.
Use the statistic

Now use any t-distribution table to find the critical value, keeping in mind that df = n - 1 = 25 - 1 = 24.
The false-negative rate is the probability of a Type II error (accepting a false null hypothesis). Now suppose the critical value that you got for the t-test above is . To compute for , calculate
.
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: p = 0.50
: p < 0.50
to 6 decimal places, while
to 6 decimal places.
Hence the critical value for a 1-sided test with is .
The rejection region is then , and the acceptance region is .
The test statistic is x = n*p = 25*0.30 = 7.5. Thus we reject the null hypothesis, and conclude that the ratio is less than 0.50.
, or

I hope you don't change your mind again....
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