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The manufacturer of an MP3 player wanted to know whether a 10% reduction in pric

ID: 3152595 • Letter: T

Question

The manufacturer of an MP3 player wanted to know whether a 10% 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

138

121

88

115

141

125

96

  

  Reduced price

   128

134

152

135

114

106

112

120

  

At the .01 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.

H0.

  Regular price

138

121

88

115

141

125

96

  

  Reduced price

   128

134

152

135

114

106

112

120

Explanation / Answer

Set Up Hypothesis
Null, Ho: u1 = u2
Alternative H1: u1 > u2
Test Statistic
X (Mean)=117.7; Standard Deviation (s.d1)=19.9
Number(n1)=7
Y(Mean)=125.1; Standard Deviation(s.d2)=15.1
Number(n2)=8
Value Pooled variance S^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
S^2 = (6*396.01 + 7*228.01) / (15- 2 )
S^2 = 305.5485
we use Test Statistic (t) = (X-Y)/Sqrt(S^2(1/n1+1/n2))
to=117.7-125.1/Sqrt((305.5485( 1 /7+ 1/8 ))
to=-7.4/9.0467
to=-0.818
| to | =0.818
Critical Value
The Value of |t | with (n1+n2-2) i.e 13 d.f is 2.65
We got |to| = 0.818 & | t | = 2.65
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value: Right Tail -Ha : ( P > -0.818 ) = 0.78594
Hence Value of P0.01 < 0.78594,Here We Do not Reject Ho

Both use Pooled StDev = 17.4847

The test statistic is . (Round your answer to 2 decimal places.)

T-Value = -0.82

The pooled variance is . (Round your answer to 2 decimal places.)