# very last doubt

• Jan 8th 2008, 10:00 AM
0123
very last doubt
I have a doubt over the way my teacher solved this exercice:

Let X be a Normal random variable N (μ, σ2= 169) with an unknown parameter μ. For testing the
hypothesis H0: μ = 28 versus H1: μ = 31 a random sample of size n = 225 is observed.
a) Consider the following rejection region: ( ){ }1107,29:...,, 2251 ≥≡ xxxR . Evaluate α (the
probability of the type I error) and β (the probability of the type II error) corresponding to the given
test.
b) Calculate the p-value corresponding to the following sample:

(32, 29, 28, 34, 27)

For the point b) my teacher wrote P[Z>=(30-28)/(13/15)]
I do not understand why she used 15 when the new sample is 5 ?
Thank you.
• Jan 8th 2008, 10:43 AM
0123
I just realize the text did not appear properly: here is the correct:

Let X be a Normal random variable N (μ, σ2= 169) with an unknown parameter μ. For testing the hypothesis H0: μ = 28 versus H1: μ = 31 a random sample of size n = 225 is observed.
a) Consider the following rejection region: R:(X_mean>= 29.1107) evaluate the probability alpha of the type I error(reject H_0 when H_0 true) and β (the probability of the type II error= accept H_0 when H_0 false) corresponding to the given test.
b) Calculate the p-value corresponding to the following sample:

(32, 29, 28, 34, 27)

Point a) is okay.
For the point b) my teacher wrote P[Z>=(30-28)/(13/15)]
I do not understand why she used 15 when the new sample is 5 ?
Thank you.

• Jan 8th 2008, 10:46 AM
colby2152
I'm not sure where you are getting a sample size of five. The sample size is $n=225$, so $\sqrt{n} = 15$
• Jan 8th 2008, 10:48 AM
0123
Quote:

Originally Posted by colby2152
I'm not sure where you are getting a sample size of five. The sample size is $n=225$, so $\sqrt{n} = 15$

Because it says:

Calculate the p-value corresponding to the following sample:

(32, 29, 28, 34, 27)
which are 5.
• Jan 8th 2008, 12:53 PM
mr fantastic
Quote:

Originally Posted by 0123
I have a doubt over the way my teacher solved this exercice:

Let X be a Normal random variable N (μ, σ2= 169) with an unknown parameter μ. For testing the
hypothesis H0: μ = 28 versus H1: μ = 31 a random sample of size n = 225 is observed.
[snip]
b) Calculate the p-value corresponding to the following sample:

(32, 29, 28, 34, 27)

For the point b) my teacher wrote P[Z>=(30-28)/(13/15)]
I do not understand why she used 15 when the new sample is 5 ?
Thank you.

You're right, clearly n = 5.
• Jan 9th 2008, 04:34 AM
colby2152
Quote:

Originally Posted by 0123
Because it says:

Calculate the p-value corresponding to the following sample:

(32, 29, 28, 34, 27)
which are 5.

I must have missed that. The new sample size is 5 rather than 225 as Mr. Fantastic pointed out.