Question

We have manufactured a product and are testing whether it is better than a competitor's product. We find that 13 of 20 people prefer our product to the competitor's product. Do we have enough evidence to declare that we have a superior product, or is there still doubt?

a. our P-value is above 10%, so there is still doubt

b. out P-value is between 5% and 10%, so there is still doubt

c. our P-value is below 5% so we feel confident that our product is better

d. we cannot answer this question with so few subjects. We would need at least 1,000 subjects before we could be confident of anything

Answer 1

In order for our product to be superior, the mean number of people using it should be more than 10.

The sample number of people using it = 13

The standard error

Now, the z-score for the sample number of 13

The P-value corresponding to Z = 1.342 is 0.089 or 8.9%.

As we can see, our P-value is between 5% and 10%. Hence, unless the significance level is known, we are still in doubt whether our product is a better product or not.

Hence, option b is correct.

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