aflacatn

2021-01-10

The Wall Street Journal reported that the age at first startup for

a. Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of

b. Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of

c. Are the standard errors of the sampling distributions different in parts (a) and (b)?

Nathaniel Kramer

Skilled2021-01-11Added 78 answers

Given that the percentage of business owners whose first venture was launched when they were 29 years old or younger is $p=0.55$ and the sample size $n=200$

The proportion's sample distribution is roughly normal if $np\Rightarrow 5\text{}and\text{}n(1\u2014p)\Rightarrow 5$.

$np=200\times 0.55$

$=110\Rightarrow 5$

$n(1\u2014p)=200\times (1\u20140.55)$

And

$=90\Rightarrow 5$

As a result, the proportion's sample distribution is normal.

The mean of the $\stackrel{\u2015}{p}\text{}is\text{}E(\stackrel{\u2015}{p}))=p$ and standard deviation of $\stackrel{\u2015}{p}\text{}is\text{}{\sigma}_{\stackrel{\u2015}{p}}=\sqrt{p(1-p)}/n$

The percentage of business owners in this context whose initial startup occurred when they were 29 years old or younger is called bar p.

The mean of $\stackrel{\u2015}{p}$ is

$E\stackrel{\u2015}{p})=p=0.55$

The standard deviation of $\stackrel{\u2015}{p}$ is

${\sigma}_{p}=\frac{\sqrt{p(1-p)}}{n}=\frac{\sqrt{0.55\times 0.45}}{200}=0.0352$

So, the proportional sampling distribution $\stackrel{\u2015}{p}$ an average number of entrepreneurs had their first business at age 29 or younger. $E(\stackrel{\u2015}{p})=0.55$ and standard deviation ${\sigma}_{p}=0.0352$

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