Onesample Hypothesis Test for p
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Key Questions

In order to conduct a onesample proportion ztest, the following conditions should be met:
 The data are a simple random sample from the population of interest.
 The population is at least 10 times as large as the sample.
#n*p>=10# and#n*(1p)>=10# , where#n# is the sample size and#p# is the true population proportion.

A one sample z test for a proportion is a test meant to evaluate if a certain proportion
#p# is equal or not to a certain value#p_0# .
The test is calculated in this way:#z_0 = (hat p  p_0)/(sqrt((p_0*(1p_0))/n)# where
#hat p# is the proportion calculated on your sample.
then, depending on which type of alternative hypotesis and value of#alpha# do you have, you accept or reject the null hypothesis depending on the value of#z_0# . 
#\hatp# : the estimated value of the parameter#p# based on your sample.#\p_0# : the real value of#p# under the null hypothesis.pvalue : formally, the probability, under the null hypothesis of obtaining the observed value or any other value wich brings more evidence to reject
#H_0# .As an example let's say you want to test if a coin toss is actually fair or heads has a larger probability. In this case you would have:
#H_0# :#p = p_0 = 0.5# vs#H_1# :#p > 0.5# , where p is the probability of the "heads" results.Then you calculate your
#\hatp# wich in this case will be the proportion of heads in your sample. Let's say you got a 0.65 proportion in your sample.Then your pvalue will be the probability under
#H_0# (this means you calculate this probability assuming it's a fair coin) of having a proportion of 0.65 or more in your sample, because the larger the proportion, we get more evidence that "heads" has more probability.Small pvalues leads us to reject
#H_0# .