The manufacturer of an MP3 player wanted to know whether a 1

The manufacturer of an MP3 player wanted to know whether a 10 percent reduction in price is enough to increase the sales of its product. To investigate, the owner randomly selected eight outlets and sold the MP3 player at the reduced price. At seven randomly selected outlets, the MP3 player was sold at the regular price. Reported below is the number of units sold last month at the sampled outlets.

  Regular price

132

126

88

117

147

122

96

  Reduced price

122

133

152

132

118

108

112

113

At the .050 significance level, can the manufacturer conclude that the price reduction resulted in an increase in sales? Hint: For the calculations, assume the \"Reduced price\" as the first sample.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   <=   0  
Ha:   u1 - u2   >   0  
At level of significance =    0.05          
As we can see, this is a    right   tailed test.      
Calculating the means of each group,              
              
X1 =    123.75          
X2 =    118.2857143          
              
Calculating the standard deviations of each group,              
              
s1 =    14.58717636          
s2 =    20.41824581          
              
Thus, the pooled standard deviation is given by              
              
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]               
              
As n1 =    8   , n2 =    7  
              
Then              
              
S =    17.52125867

Hence, the pooled variance is

S^2 =    306.9945054 [ANSWER, POOLED VARIANCE]
      
              
Thus, the standard error of the difference is              
              
Sd = S sqrt (1/n1 + 1/n2) =    9.068112875          
              
As ud = the hypothesized difference between means =    0   , then      
              
t = [X1 - X2 - ud]/Sd =    0.602582455   [ANSWER, TEST STATISTIC]