Question

Suppose that we are interested in learning about the effect of a new gasoline detergent additive on automobile mileage. We formulate a statistical hypothesis test and collect two samples. Which of the following situation is most suited for a paired T test?

A. Sample 1 consists of 12 Toyota Camry running on gasoline without the additive, and sample 2 consists of another 12 Toyota Camry running on gasoline with the additive.

B. Sample 1 consists of 12 cars (of different makes and models) running on gasoline without the additive, and sample 2 consists of another 12 cars (of different makes and models) running on gasoline with the additive.

C. Sample 1 consists of 12 Toyota Camry running on gasoline without the additive, and sample 2 consists of 12 Accord Honda running on gasoline with the additive.

D. Sample 1 consists of 12 cars (of different makes and models) running on gasoline without the additive, and sample 2 consists of the same 12 cars running on gasoline with the additive.

Answer 1

Solution:

Paired t-test is used, when we have repeated measures i.e. we have two samples but the sampling units in both the samples are same and information is collected on the same subjects in two different conditions and we want to test the equality of means.

Since, in option (D), 12 cars (of different makes and models) running on gasoline without the additive, and sample 2 consists of the same 12 cars running on gasoline with the additive, i.e. we have information on same 12 cars in two different conditions (with and without additive), therefore this situation is most suited for paired t-test.

Hence, the situation given in option (D) is most suited for a paired t-test.

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