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.)Related Questions
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