Exhibit 10.5. A producer of fine chocolates believes that the sales of two varie

Question

Exhibit 10.5.

A producer of fine chocolates believes that the sales of two varieties of truffles differ significantly during the holiday season. The first variety is milk chocolate, while the second is milk chocolate filled with mint. It is reasonable to assume that truffle sales are normally distributed with unknown but equal population variances. Two independent samples of 18 observations each are collected for the holiday period. A sample mean of 12 million milk chocolate truffles sold with a sample standard deviation of 2.5 million. A sample mean of 13.5 million truffles filled with mint sold with a sample standard deviation of 2.3 million. Use milk chocolate as population 1 and mint chocolate as population 2.

Refer to Exhibit 10.5. What is the appropriate decision given a 5% level of significance?

A) Conclude that the average milk chocolate and mint chocolate sales differ since the p-value is greater than 0.05.

B) Conclude that the average milk chocolate and mint chocolate sales do not differ since the p-value is less than 0.05.

C) Do not conclude that the average milk chocolate and mint chocolate sales differ since the p-value is greater than 0.05.

D) Do not conclude that the average milk chocolate and mint chocolate sales do not differ since the p-value is less than 0.05.

Explanation / Answer

The statistical software output for this problem is:

Two sample T summary hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 0
(without pooled variances)

Hypothesis test results:

Therefore,

We do not conclude that the average milk chocolate and mint chocolate sales differ since the p-value is greater than 0.05.

Option C is correct.

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