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 regular and reduced prices at the randomly selected outlets.

Regular price	131	122	102	115	121	124	114
Reduced price	125	136	151	132	112	123	131	133

  Click here for the Excel Data File

At the 0.100 significance level, can the manufacturer conclude that the price reduction resulted in an increase in sales? Hint: For the calculations, assume reduced price as the first sample.

1. Compute the pooled estimate of the variance. (Round your answer to 3 decimal places.)

2. Compute the test statistic. (Round your answer to 2 decimal places.)

3. State your decision about the null hypothesis.

• Reject H₀

• Fail to reject H₀

Answer 1

Let denote the mean number of units sold at reduced and regular prices respectively.

To test: Vs   

The appropriate statistical test to test the above hypothesis would be an Independent sample t-test.

But before running this test, we must ensure that the data satisfies the assumptions of this test:

- The data is continuous

- The observations are from a simple random sample

- The data is normally distributed

- Homogeneity of Variance  

Assuming that all the assumptions are satisfied:

The test statistic is given by:

Computing the mean and standard deviation,

a. Pooled variance can be computed using the formula:

= 107.507

b. The test statistic is obtained as:

The p-value of the test statistic can be obtained using the excel function:

We get p-value = 0.022

Since, the p-value of the test 0.022 < 0.05 is significant, we may reject the null at 5% level. We may conclude that the data provides sufficient evidence to support the claim that the price reduction resulted in an increase in sales.