Question

Suppose that a researcher is planning a new study on hemoglobin levels amongst women under 25 years old. Previous research suggest that the standard deviation of hemoglobin is 0.7 g/dl. In the new study the research wants to have the standard error for the sample mean to be no more than 0.05 g/dl. Find the required sample size for the new study.

Answer 1

Answer:

A sample size of at least 531 is required.

Step-by-step explanation:

We are lacking the confidence level to solve this question, so i am going to use a 90% confidence level.

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$.

So it is z with a pvalue of $1-0.05 = 0.95$, so $z = 1.645$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

Find the required sample size for the new study.

A sample size of at least n is required.

n is found when $M = 0.05$

We have that $\sigma = 0.7$

So

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.05 = 1.645*\frac{0.7}{\sqrt{n}}$

$0.05\sqrt{n} = 1.645*0.7$

$\sqrt{n} = \frac{1.645*0.7}{0.05}$

$(\sqrt{n})^{2} = (\frac{1.645*0.7}{0.05})^{2}$

$n = 530.4$

Rounding up

A sample size of at least 531 is required.