# Questions regarding hypothesis testing

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• #49756

lonelysin
Participant

Hi guys,I have a question regarding hypothesis testing but I believe it it incomplete. Below is the question.”A pilot study indicates that the standard deviation of a particular random variable X is 1.25. How large a sample is required to testH(0) : u = 20
H(1) : u > 20 20 20at the alpha=0.05 and beta=0.05 level if it is important to be able to distinguish between u=20 and u=21??
Does anyone know how to solve the above problem? Any examples?
Rgds,
Lonelysin

0
#170466

d
Participant

From the information given,
-Significance level,
a = 0.05
-Power = 1-b
= 1 – 0.05 = 0.95
-Difference in means, d =21-20= 1
-Standard Deviation, s
= 1.25
Sample size = 19

0
#170503

lonelysin
Participant

Dear Pam,which formula you use to calculate the Power?
Also, how do you get 19?Thanks.

0
#170513

Participant

I was able to recreate what Pam’s answer was in Minitab.
Here are the steps:
Open Minitab
Click Stat / Power and Sample Size / 1-sample t
In Differences field input a 1
In Power Values field input .95
In Standard Deviation Field input 1.25
Click Options Button in this same menu
Under Alternate Hypothesis Click Greater than radio button
Significance Level field input .05 if it is not already there by default
Click Ok and Ok
go to the minitab session window and you should see:

1-Sample t Test
Testing mean = null (versus > null)
Calculating power for mean = null + difference Alpha = 0.05 Assumed standard deviation = 1.25
Sample   Target
Difference   Size    Power    Actual Power
1        19      0.95    0.956078
Hope this helps.

0
#170515

Pramod
Participant

Hi Engine,
I did work it out in Minitab, you reply sure helps. Any idea about the formula that is used to calculate the sample size?
Also I would like to caluclate the sample sizes for populations which do not follow a normal distribution, how is it calculated?

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#170517