Question

in a survey of 711 lesbian, gay, bisexual, or transgender adults in a certain country, 427 said that they consider themselves bisexual. construct a 90% confidence interval for the population proportion. interpret the results. a 90% confidence interval for the population proportion is (0.570, 0.631). (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 90% of lesbian, gay, bisexual, or transgender adults consider themselves bisexual. b. with 90% 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. c. with 90% 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. d. with 90% 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.

Explanation:

A confidence interval for a population proportion gives a range of values within which the true population proportion is likely to lie. A 90% confidence interval means that if we were to take many samples and construct confidence intervals in the same way, about 90% of those intervals would contain the true population proportion. Option A is incorrect because it misinterprets the confidence interval as referring to a percentage of the population (90% of adults), not the confidence in capturing the population proportion. Option C is wrong as it refers to the wrong group (those who do not consider themselves bisexual). Option D is incorrect because it refers to the sample proportion, while confidence intervals are about the population proportion. Option B correctly interprets the 90% confidence interval as being about the population proportion.

Answer:

B. With 90% 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.