People say that coke and pepsi taste different, but are they really that different? a researcher randomly samples people and has each do a blind taste-test to see if they can really identify which of two drinks they taste is coke and which is pepsi. the researcher will look at the proportion of the random sample that correctly identifies coke and peps in order to come to a conclusion.

a. if the researcher samples 40 people and uses a null hypothesis of p0 = .5, can the researcher carry out a valid 1-sample proportion test?

b. if the researcher samples 10 people and uses a null hypothesis of p0 = .5, can the researcher carry out valid a 1-sample proportion test?

c. if the researcher samples 20 people and uses a null hypothesis of p0 = .9, can the researcher carry out a valid 1-sample proportion test?

d. if the researcher samples 100 people and uses a null hypothesis of of p0 = .9, can the researcher carry out a valid 1-sample proportion test?

e. if you use a null hypothesis of p = .05, what is the smallest sample size you can use to carry out a valid 1-sample proportions test?