Question

The difference between the sample means of two populations is 34.6, and the standard deviation of the difference between sample means is 11.9. What is the 95% confidence interval

Answer 1

Answer: -23.8,23.8

Explanation:

Answer 2

The required interval is
`10.8\leq CI \leq 58.4`

Explanation:

Given : The difference between the sample means of two populations is 34.6, and the standard deviation of the difference between sample means is 11.9.

To find : What is the 95% confidence interval lies between ?

Solution :

Let
`\mu_1,\mu_2` were two sample means.

The difference between the sample means of two populations is 34.6

i.e.
`\mu_1-\mu_2=34.6=\mu`

Let
`\sigma_1,\sigma_2` were two standard deviation.

The difference between the standard deviation of two populations is 11.9

i.e.
`\sigma_1-\sigma_2=11.9=\sigma`

The confidence interval at 95% is 2 dimension,

So, The formula to find class interval is

`\mu-2\sigma\leq CI \leq \mu+2\sigma`

`34.6-2(11.9)\leq CI \leq 34.6+2(11.9)`

`34.6-23.8\leq CI \leq 34.6+23.8`

`10.8\leq CI \leq 58.4`

Therefore, The required interval is
`10.8\leq CI \leq 58.4`