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

The required amount of mice is 11.82 gram.

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=(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=(x-3)/(4.5)`

`1.96* 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.