Question

GSK is testing a new cough syrup formula which they hope will reduce the proportion of users who experience acid reflux while taking the syrup. Using the older formulation, 15% of all users experienced reflux. As part of their pre-sales work, the research team decides to conduct a hypothesis test to check their theory. A large number of patients will be tested, and the results used to make a conclusion about the true proportion of cough syrup users who have the problem. If is rejected, then the scientists will be convinced that their new product works the way they hoped it would.

A.) Set up hypotheses for their test, defining any parameters that you use. No calculations required here!

B.) In the context of the problem, describe a Type I error – that is, what mistaken belief would they have about the unknown parameter – and also discuss the consequences to GSK and to the public of this error. No calculations required here either!

Answer 1

A)

Ho :   Mean true proportion of users who experience acid reflux while taking the syrup is 15%
Ha :   Mean true proportion of users who experience acid reflux while taking the syrup is less than 15%

b)
Type 1 error when you reject the hypothesis when you should not or we can say rejection of a true null hypothesis.

It means Mean true proportion of users who experience acid reflux while taking the syrup is actually 15% but we have considered that Mean true proportion of users who experience acid reflux while taking the syrup is less than 15%.

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