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Binomial hypothesis testing question s2

I have been given a hypothesis testing question to do but with no situation or context.
Null Hypothesis: p=0.25
Alternate Hypothesis: p>0.25
N=10
x=5.
sig level: 5%

can someone explain why I would need to find p(x is greater or equal to 5) please.
Reply 1
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kevvvvvv
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@Zacken
Reply 2
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Zacken
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Original post by kevvvvvv
I have been given a hypothesis testing question to do but with no situation or context.
Null Hypothesis: p=0.25
Alternate Hypothesis: p>0.25
N=10
x=5.
sig level: 5%

can someone explain why I would need to find p(x is greater or equal to 5) please.


The null hypothesis is rejected if P(X >= x) <= 5% (since the alternate hypothesis is p > 0.25, if it was p < 0.25, you'd do P(X<= x))

In this case, x = 5. So P (X >= 5) - then use binomial tables with P (X >= 5) = 1 - P(X <= 4).
X ~ B(10, p)

Sorr for lack of LaTeX I'm not home and typing on my phone is shite
Reply 3
Avatar for kevvvvvv
kevvvvvv
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@Student403
Reply 4
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kevvvvvv
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Original post by Zacken
The null hypothesis is rejected if P(X >= x) <= 5% (since the alternate hypothesis is p > 0.25, if it was p < 0.25, you'd do P(X<= x))

In this case, x = 5. So P (X >= 5) - then use binomial tables with P (X >= 5) = 1 - P(X <= 4).
X ~ B(10, p)

Sorr for lack of LaTeX I'm not home and typing on my phone is shite


no worries that makes sense thank you
Reply 5
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Zacken
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Original post by kevvvvvv
no worries that makes sense thank you


Yay, no problem! :smile:
Reply 6
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Ayman!
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Original post by Zacken
...


I've had this problem doing S2 hypothesis testing. While testing a discrete distribution, I usually draw a normal curve just to make things easier to understand. For example, if they're asking to find the critical values of X ~ B(30, 0.25), I'll draw a normal curve with the mean = np just for reference. Our school teacher taught us this method, but I'm worried that the examiner will assume that I don't know the difference between a discrete and a continuous distribution. Would this affect the way they mark it, you think (assuming my working is all correct)?
Reply 7
Avatar for Zacken
Zacken
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Original post by aymanzayedmannan
I've had this problem doing S2 hypothesis testing. While testing a discrete distribution, I usually draw a normal curve just to make things easier to understand. For example, if they're asking to find the critical values of X ~ B(30, 0.25), I'll draw a normal curve with the mean = np just for reference. Our school teacher taught us this method, but I'm worried that the examiner will assume that I don't know the difference between a discrete and a continuous distribution. Would this affect the way they mark it, you think (assuming my working is all correct)?


Nah, definitely not. You might want to scratch a line through it once you're done with the question for your own peace of mind, though.
Original post by kevvvvvv
I have been given a hypothesis testing question to do but with no situation or context.
Null Hypothesis: p=0.25
Alternate Hypothesis: p>0.25
N=10
x=5.
sig level: 5%

can someone explain why I would need to find p(x is greater or equal to 5) please.


If the alternative hypothesis had been p not = 0.25, you would have to compare the mean np with the x value. np = 10 x 0.25 = 2.5 x = 5 is bigger than the mean, so you would still have looked at P(X>=5) since you want a small probability to compare with half of 5%.
(edited 8 years ago)
it is a single tailed test so use all of the 5% in the comparison stage.
Reply 10
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Zacken
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Original post by kevvvvvv


Avoid tagging multiple users, if possible. One may already be answering your question and it would be a duplication of effort. :smile:

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