# Ststistics: Normal Distribution

*Please see attachment for case study.

Questions:

(a) What are the observational units and variable units of interest in this study? Also specify the population or process of interest.

(b) State and null and an alternative hypothesis about the value of pi (in words and symbols)

(c) We can assess the strength of evidence against the null hypothesis by treating 897 current athletes as a random sample from the process of athlete determination at Brown. If we initially give the university the benefit of the doubt and assume the nully hypothesis is true, does the Central Limit Theorem for a sample proportion apply here? Explain.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

a) Observational units:the 897 student

Population of interest:undergrad women

unknown param of interest:proportion of undergrad women

b)Ho: Ï€=.51

Ha: Ï€ not =.51

c)If we assume that Ï€=.51 , and suppose that the CLT apply here

then the mean of the sample proportion should be Ï€ and the standard deviation should be sqrt( Ï€(1- Ï€)) .Replacing Ï€ with .51 we get that

the saple proportion has mean .51 and standard deviation = .4998

But the proportion of the sample is .38 which falls within one standard deviation of the mean.

So we can apply CLT

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