Chapter 11.5, Problem 26E

a.

To determine

To calculate:

Value of $n$ for the given condition.

Answer to Problem 26E

  $n$ should be large than $9$ for $p=0.5$ .

Explanation of Solution

Given information:

  $n>9\left(\frac{1-p}{p}\right)$

  $p=0.5$

Calculation:

It is given that,

  $n>9\left(\frac{1-p}{p}\right)$

And value of $p$ given is $0.5$ .

So after putting the $p=0.5$ in above equation,

  $\begin{array}{l}n>9\left(\frac{1-p}{p}\right)\\ =n>9\left(\frac{1-0.5}{0.5}\right)\\ =9=P\end{array}$

Hence, Value of $n$ for the given condition is $9$ .

Therefore, $n$ should be large than $9$ for $p=0.5$ .

b.

To determine

To calculate:

Value of $n$ for the given condition.

Answer to Problem 26E

  $n$ should be large than $891$ for $p=0.01$ .

Explanation of Solution

Given information:

  $n>9\left(\frac{1-p}{p}\right)$

  $p=0.01$

Calculation:

It is given that,

  $n>9\left(\frac{1-p}{p}\right)$

And value of $p$ given is $0.01$ .

So after putting the $p=0.01$ in above equation,

  $\begin{array}{l}n>9\left(\frac{1-p}{p}\right)\\ =n>9\left(\frac{1-0.01}{0.01}\right)\\ =n>9\left(\frac{0.99}{0.01}\right)\\ =n>9\left(99\right)\\ =891=P\end{array}$

Hence, Value of $n$ for the given condition is $891$ .

Therefore, $n$ should be large than $891$ for $p=0.01$ .

c.

To determine

To explain:

Conclusion from the part $\left(a\right)$ and part $\left(b\right)$

Answer to Problem 26E

Smaller the percentage , the larger the sample size required to be to represent the population.

Explanation of Solution

Given information:

  $n>9\left(\frac{1-p}{p}\right)$

  $p=0.5,p=0.01$

From the result of part $\left(a\right)$ and part $\left(b\right)$ , one can conclude that the smaller the percentage of people with a certain characteristics, the larger the sample size required to be to represent the population.