# CLT and probability

A researcher conducted an experiment to evaluate if the proportion of supporters for the most corrupted party in the country is equal to 40% (null hypothesis). The alternative hypothesis is that the proportion is larger than 40%. In his sample, she observed:

•An average proportion of 48% of supporters
•An standard error ( ˆσ /sqrt n) of 3.1
•A p-value of 0.005 (approximately)

Assume you can use the CLT because the sample size is large enough. Answer true or false and explain your answer.

(a) If the null hypothesis is right, there is a 0.5% chance of observing a value equal to or larger than 48%.
(b)  The probability of the null hypothesis given the data is 0.5%.

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Erdos
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• If possible, set a later deadline for your questions in future.

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