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

Question

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. At the.010 significance level, can the manufacturer conclude that the price reduction resulted in an increase in sales? The pooled variance is The test statistic is

Explanation / Answer

Set Up Hypothesis
Null, Ho: u1 = u2
Alternative , H1: u1 != u2
Test Statistic
X (Mean)=118.5714; Standard Deviation (s.d1)=20.0155
Number(n1)=7
Y(Mean)=124.125; Standard Deviation(s.d2)=15.151
Number(n2)=8
a.
Value Pooled variance S^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
S^2 = (6*400.6202 + 7*229.5528) / (15- 2 )
S^2 = 308.507
b.
we use Test Statistic (t) = (X-Y)/Sqrt(S^2(1/n1+1/n2))
to=118.5714-124.125/Sqrt((308.507( 1 /7+ 1/8 ))
to=-5.5536/9.0904
to=-0.6109
| to | =0.6109
c.
Critical Value
The Value of |t | with (n1+n2-2) i.e 13 d.f is 1.771
We got |to| = 0.6109 & | t | = 1.771
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho

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