. A history museum just opened an exhibit about the mathematics of ancient Greece. For one week aer
the exhibit opens, a museum employee randomly selects people leaving the museum and asks them to
identify their favorite exhibit. Out of the 512 people polled, 204 of them say the ancient Greece math
exhibit was their favorite. Construct a 90% confidence interval and interpret it in context.
We can use the formula for a confidence interval for a proportion:
CI = p̂ ± z*√(p̂(1-p̂)/n)
where:
p̂ = proportion of people who said the ancient Greece math exhibit was their favorite = 204/512 = 0.3984
z = the z-score for a 90% confidence level, which can be found using a standard normal distribution table or calculator. For a 90% confidence level, z = 1.645.
n = sample size = 512
Plugging in these values, we get:
CI = 0.3984 ± 1.645*√(0.3984(1-0.3984)/512)
CI = 0.3984 ± 0.048
So the 90% confidence interval for the proportion of people who said the ancient Greece math exhibit was their favorite is (0.3504, 0.4464).
Interpretation: We are 90% confident that the true proportion of people who said the ancient Greece math exhibit was their favorite is between 0.3504 and 0.4464. This means that if we were to repeat this sampling process many times and construct a 90% confidence interval each time, about 90% of those intervals would contain the true proportion of people who liked the exhibit. Therefore, we can say with 90% confidence that somewhere between 35.04% and 44.64% of all museum visitors would say the ancient Greece math exhibit was their favorite.