Question

For each situation described, indicate whether it makes more sense to use a relatively large significance level (such as \(\alpha=0.10\) ) or a relatively small significance level (such as \(\alpha=0.01\) ). A pharmaceutical company is testing to see whether its new drug is significantly better than the existing drug on the market. It is more expensive than the existing drug. Which significance level would the company prefer? Which significance level would the consumer prefer?

Short answer

The pharmaceutical company would prefer a larger significance level (such as \(\alpha = 0.10\)) because it increases the chances of confirming their claim that the new drug is better. On the contrary, the consumer would prefer a smaller significance level (such as \(\alpha = 0.01\)) to minimize the risk of believing that the new (and more expensive) drug is better when it might not be.

Step-by-step solution

Understand the role of significance level

Statistically, the significance level, also denoted as \(\alpha\), is the probability of rejecting the null hypothesis when it is actually true. This is known as a false positive or Type I error. A smaller value of \(\alpha\) means fewer chances of making a type I error, whereas a larger value of \(\alpha\) makes it easier to reject the null hypothesis, hence increasing the chances of a type I error.

Analyze the pharmaceutical company's position

The pharmaceutical company wants to prove that the new drug is significantly better. So, they would prefer the larger significance level of \(\alpha = 0.10\), which increases the chances of them rejecting the null hypothesis (that the new drug is not better). They would run the risk of a Type I error (false positive), i.e., believing the new drug is better, when it actually is not.

Analyze the consumer's position

On the other hand, consumers would prefer a more cautious approach because they would want to minimize the risk of believing the new drug is better when it actually isn't, especially given the new drug is more expensive. Therefore, they would prefer the smaller significance level of \(\alpha = 0.01\).