Question

in a survey of 668 lesbian, gay, bisexual, or transgender adults in a certain country, 385 said that they consider themselves bisexual. construct a 99% confidence interval for the population proportion. interpret the results. a 99% confidence interval for the population proportion is (0.527, 0.625) (round to three decimal places as needed.) interpret your results. choose the correct answer below. a. the endpoints of the given confidence interval show that 99% of lesbian, gay, bisexual, or transgender adults consider themselves bisexual. b. with 99% confidence, it can be said that the sample proportion of lesbian, gay, bisexual, or transgender adults who consider themselves bisexual is between the endpoints of the given confidence interval. c. with 99% confidence, it can be said that the population proportion of lesbian, gay, bisexual, or transgender adults who consider themselves bisexual is between the endpoints of the given confidence interval. d. with 99% probability, the population proportion of lesbian, gay, bisexual, or transgender adults who do not consider themselves bisexual is between the endpoints of the given confidence interval.

Explanation:

A confidence interval for a population proportion gives a range of values within which the true population proportion is likely to lie. A 99% confidence interval means that if we were to take many samples and construct confidence intervals in the same way, about 99% of those intervals would contain the true population proportion. Option C correctly interprets the confidence interval as being about the population proportion. Option A is incorrect because it misinterprets the confidence interval as referring to a percentage of the population (not about the interval containing the proportion). Option B is wrong as it refers to the sample proportion (the confidence interval is for the population proportion). Option D is incorrect as it refers to the proportion of those who do not consider themselves bisexual (the original data is about those who do consider themselves bisexual).

Answer:

C. With 99% confidence, it can be said that the population proportion of lesbian, gay, bisexual, or transgender adults who consider themselves bisexual is between the endpoints of the given confidence interval.