Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of p where p 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(p) = σ(p) = (b) Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of p where p 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.

The missing part of the question is highlighted in bold format

The Wall Street Journal reported that the age at first startup for 90% of entrepreneurs was 29 years of age or less and the age at first startup for 10% of entrepreneurs was 30 years of age or more.

Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of p where p 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(p) = σ(p) = (b) Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of p where p 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.

(a)

np = 180

n(1-p) = 20

E(p) = p = 0.9

σ(p) = 0.0212

(b)

np =  20

n(1 - p) = 180

E(p) = p = 0.1

σ(p) = 0.0212

Step-by-step explanation:

From the given information:

Let consider p to be the sample proportion of entrepreneurs whose first startup was at 29 years of age or less

So;

Given that :

p = 90%    i.e  p = 0.9

sample size n = 200

Then;

np = 200 × 0.9 = 180

n(1-p) = 200 ( 1 - 0.9)

= 200 (0.1)

= 20

Since np and n(1-p) are > 5 ; let assume that the data follows a normal distribution ;

Then:

The expected value of the sampling distribution of p =  E(p) = p = 0.9

Variance

The standard error of  σ(p) =

= 0.0212

(b)

Here ;

p is now the sample proportion of entrepreneurs whose first startup was at 30 years of age or more

p = 10%   i.e p = 0.1

sample size n = 200

Then;

np = 200 × 0.1 = 20

n(1 - p) = 200 (1 - 0.1 )  = 180

Since np and n(1-p) are > 5 ; let assume that the data follows a normal distribution ;

Then:

The Expected value of the sampling distribution of p = E(p) = p = 0.1

Variance

The standard error of  σ(p) =

= 0.0212

the value of x is 28.2

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