# What is the smallest value of r that gives a test of size not exceeding 0.05?

#### NewbieStudent

##### New Member
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I've been given a question that I don't understand.

Question: Consider a test which rejects H0 if the number of observed successes is ≥r≥r , where r is some number. What is the smallest value of r that gives a test of size not exceeding 0.05?

We have been given:

o=50 ,for 50 observations
H0=p=1/2

I know that a test size is the probability of committing a type 1 error, where we falsely reject the null hypothesis when the null hypothesis is true. This happens 5% of the time if our p-value cut off is 0.05.

What I'm not sure about is
: "What is the smallest value of r that gives a test of size not exceeding 0.05?"
Because if r is just some random number that hasn't been specified, what's stopping me from putting in a large number for r , such as 49?

I've attempted it by using:

mu=np

SD=sqrt(np(1−p))

a=0.05

Using RStudios for computation I did the following:

qnorm(0.95,mean=50*0.5,sd=sqrt(50*0.5*0.5)

But this gives me the test value. Because i'm unsure about what the question means, i'm not sure if this is the correct way of finding the answer.

#### NewbieStudent

##### New Member
Yup, i wasn't sure how to delete this post after Glen.b posted on stats exchange.