Question

Two random samples are selected from two independent populations. A summary of the sample sizes, sample means, and sample standard deviations is given below:

n1=43, x¯1=59.1, ,s1=5.9

n2=40, x¯2=72.6, s2=11

Find a 99% confidence interval for the difference μ1−μ2 of the means, assuming equal population variances.

_________<μ1−μ2<____________

Answer 1

We have given here,                  
                  
For sample 1                  
                  
Sample mean =59.1      
Sample standard deviation=5.9      
Sample size=43      
                  
For sample 1                  
                  
Sample mean =72.6      
Sample standard deviation=11      
Sample size=40      
                  
Level of significance=1-0.99=0.01      
Degree of freedom =81      
t critical value (by using t table) =2.64
                  

The pooled standard deviation formula is                   

=8.74   
                  

  
Confidence interval formula is                  

=(-18.56,-8.44)

Therefore,

-18.6 <μ1−μ2< -8.4