The Wall Street Journal reported that the age at first startup for 65% of entrepreneurs was 29 years of age or less and the age at first startup for 35% of entrepreneurs was 30 years of age or more.
(a) Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of p̄ where p̄ is the sample proportion of entrepreneurs whose first startup was at 29 years of age or less. If required, round your answers to four decimal places.
np =
n(1-p) =
E(p̄) =
σ(p̄) =
(b) Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of p̄ where p̄ is now the sample proportion of entrepreneurs whose first startup was at 30 years of age or more. If required, round your answers to four decimal places.
np =
n(1-p) =
E(p̄) =
σ(p̄) =
(c) Are the standard errors of the sampling distributions different in parts (a) and (b)?
Justify your answer.