# question on research problem

#### ajk003

##### New Member
I'm having some trouble with conducting a hypothesis test:

Suppose it has been esablished that musicians, as a general population, have a mean IQ of 100, with a standard deviation of 35. Researchers suspect that IQ scored of piano players differ from those of other musicians. They collect a random sample of 27 piano players and find that the mean IQ of these musicians is 111.
The level of significance is 0.05. Determine whether the IQ scores of piano players differ from those of other musicians.

So, for the problem they give me a sample of 27 piano players. Would 27 be the "n" and would I solve for the standard deviation of sample using that number? I know I have to solve for the standard deviation of error but I do not know what I should substitute for the standard deviation.

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#### JohnM

##### TS Contributor
Seems like something is missing.....

What you could do is determine the probability of getting a sample mean of 111 from a population with mean = 100 and sigma = 35.

But you would need to assume that the standard deviation of the sample of 27 was the same as the standard deviation of the population, which may be a stretch...

Z = (111 - 100) / (35/sqrt(27))
= 1.633

P(Z >= 1.633) = .051 --> do not reject Ho