Suppose strep resistance rates in all cities across the country are actually 0.0

Question

Suppose strep resistance rates in all cities across the country are actually 0.05.

a) If samples are taken in a particular city to produce a 90% confidence interval for the proportion of all strep cultures in the city that are resistant to antibiotics, what is the probability that the 90% confidence interval succeeds in capturing the true population proportion for that city?

b) If samples are taken in 100 cities across the country, to produce 100 90% confidence intervals for the proportion of all strep cultures in each city that are resistant to antibiotics, about how many of the intervals should succeed in capturing the city's true population proportion?

c) About how many of the 100 90% confidence intervals would fail to capture the true population proportion?

Explanation / Answer

a) The 90% confidence interval means there are 90% chances that all the 90% confidence intervals based on all the different samples from the same city, the true proportion will lie between this interval. So the answer of part a) is 0.90

b) here we assume that the strep resistance rates in all cities across the country are actually 0.05. So 90% confidence intervals from the samples are taken in 100 cities 90 or more than 90 of them should succeed in capturing the city's true population proportion.

c) About 10 or less out of 100 90% confidence intervals would fail to capture the true population proportion.

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