Answer:
The required interval is [tex]10.8\leq CI \leq 58.4[/tex]
Step-by-step 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 [tex]\mu_1,\mu_2[/tex] were two sample means.
The difference between the sample means of two populations is 34.6
i.e. [tex]\mu_1-\mu_2=34.6=\mu[/tex]
Let [tex]\sigma_1,\sigma_2[/tex] were two standard deviation.
The difference between the standard deviation of two populations is 11.9
i.e. [tex]\sigma_1-\sigma_2=11.9=\sigma[/tex]
The confidence interval at 95% is 2 dimension,
So, The formula to find class interval is
[tex]\mu-2\sigma\leq CI \leq \mu+2\sigma[/tex]
[tex]34.6-2(11.9)\leq CI \leq 34.6+2(11.9)[/tex]
[tex]34.6-23.8\leq CI \leq 34.6+23.8[/tex]
[tex]10.8\leq CI \leq 58.4[/tex]
Therefore, The required interval is [tex]10.8\leq CI \leq 58.4[/tex]