Question

A new drug for migraine headaches has been introduced to the market. You would like to know if migraine patients prefer the old drug or the new drug. So, you sample 190 patients that have used both drugs and you find that 52% of the sampled patients prefer the new drug, 48% of the patients prefer the old drug. Find the 90% confidence limit for the proportion of all patients that prefer the new drug. Can you be 90% confident that a majority of all the patients prefer the new drug?

using confidence limits for proportions

Answer 1

Given

^{P = 0.52, n = 190, z = 1.645 [Using Excel =normsinv(0.10/2)]}

=.52± 1.645 √.52(1-.52)
                     √190
=0.52±0.0596
=0.46 to 0.58

^{The confidence interval is 0.46 to 0.58}

^{The smallest interval is 0.46 which is less than the 0.5, so no, we cannot be 90% confident that a majority of the patients will prefer the new drug.}

^{Please do the comment for any doubt or clarification. Please upvote if this helps you out. Thank You!}