Arandom sample of size n1= 25, taken from a normal population with a standard deviation σ1= 5, has a mean x1= 80. a second random sample of size n2=36, taken from a different normal population with a standard deviation σ2=3, has a mean x1= 75. find a 94% confidence interval for μ1-μ2.

The 94% confidence interval would be given by

Step-by-step explanation:

Previous concepts  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

represent the sample mean 1

represent the sample mean 2

n1=25 represent the sample 1 size  

n2=36 represent the sample 2 size  

sample standard deviation for sample 1

sample standard deviation for sample 2

parameter of interest.

The confidence interval for the difference of means is given by the following formula:  

(1)  

The point of estimate for is just given by:

Since the Confidence is 0.94 or 94%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.03,0,1)".And we see that  

The standard error is given by the following formula:

And replacing we have:

Confidence interval

Now we have everything in order to replace into formula (1):  

So on this case the 94% confidence interval would be given by  

75%

step-by-step explanation: