Question

Assuming that it is known from previous studies that σ = 4.5 grams, how many mice should be included in our sample if we wish to be 95% confident that the mean weight of the sam- ple will be within 3 grams of the population mean for all mice subjected to this protein diet?

Answer 1

Answer:

The required amount of mice is 11.82 gram.

Step-by-step explanation:

Given : Assuming that it is known from previous studies that σ = 4.5 grams. If we wish to be 95% confident that the mean weight of the sample will be within 3 grams of the population mean for all mice subjected to this protein diet.

To find : How many mice should be included in our sample?

Solution :

The formula used in the situation is

$z=\frac{x-\mu}{\sigma}$

Where, z value at 95% confidence interval is z=1.96

$\mu=3$ gram is the mean of the population

$\sigma=4.5$ gram is the standard deviation of the sample

Substituting the value, to find x sample mean

$1.96=\frac{x-3}{4.5}$

$1.96\times 4.5=x-3$

$8.82=x-3$

$x=8.82+3$

$x=11.82$

Therefore, The required amount of mice is 11.82 gram.