The manufacturer of an MP3 player wanted to know whether a 10 percent reduction
ID: 3429578 • Letter: T
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.
Regular price
134
126
88
119
143
127
96
Reduced price
122
137
152
136
117
107
112
111
At the .010 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.
Regular price
134
126
88
119
143
127
96
Reduced price
122
137
152
136
117
107
112
111
Explanation / Answer
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? Hint: For the calculations, assume the Reduced price as the first sample.
Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.01
Population 1 Sample
Sample Size
8
Sample Mean
124.25
Sample Standard Deviation
15.81816316
Population 2 Sample
Sample Size
7
Sample Mean
119
Sample Standard Deviation
20.01665973
Intermediate Calculations
Population 1 Sample Degrees of Freedom
7
Population 2 Sample Degrees of Freedom
6
Total Degrees of Freedom
13
Pooled Variance
319.6538
Standard Error
9.2532
Difference in Sample Means
5.2500
t Test Statistic
0.5674
The pooled variance is . (Round your answer to 2 decimal places. =319.65
The test statistic is = 0.5674
Upper-Tail Test
Upper Critical Value
2.6503
Calculated t=0.5674 < table value .
Null hypothesis is not rejected.
There is insufficient information in the data for the manufacturer to conclude that the price reduction resulted in an increase in sales.
Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.01
Population 1 Sample
Sample Size
8
Sample Mean
124.25
Sample Standard Deviation
15.81816316
Population 2 Sample
Sample Size
7
Sample Mean
119
Sample Standard Deviation
20.01665973
Intermediate Calculations
Population 1 Sample Degrees of Freedom
7
Population 2 Sample Degrees of Freedom
6
Total Degrees of Freedom
13
Pooled Variance
319.6538
Standard Error
9.2532
Difference in Sample Means
5.2500
t Test Statistic
0.5674
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