A market research firm supplies manufacturers with estimates

A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. A random sample of  36 stores this year shows mean sales of 78 units of a small appliance with a standard deviation of 14 units. During the same point in time last year, a random sample of 49 stores had mean sales of 93 units with standard deviation 9 units.  

It is of interest to construct a 95 percent confidence interval for the difference in population means 12, where 1 is the mean of this year\'s sales and 2 is the mean of last year\'s sales.

Enter values below rounded to three decimal places.

(a) The estimate is:   .

(b) The standard error is:   .

Solution

A)

As  
              
X1 =    78          
X2 =    93          

Then the point estimate is

X1 - X2 = 78 - 93 = -15 [ANSWER]

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b)
              
As          
              
s1 =    9          
s2 =    14          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    49          
n2 = sample size of group 2 =    36          

Thusm

sD =    2.664114425   [ANSWER, STANDARD ERROR]