Question

eric randomly surveyed 150 adults from a certain city and asked which team in a contest they were rooting for, either north high school or south high school. from the results of his survey, eric obtained the following 95% confidence interval for the proportion of all adults in the city rooting for north high, (0.52,0.68). interpret this confidence interval. choose the correct answer below. a. between 52% and 68% of adults in this city will root for north high school 95% of the time. b. theres a 95% chance that between 52% and 98% of all adults in this city will root for north high school. c. we are 95% sure that between 52% and 68% of all adults in this city will root for north high school. d. we are 95% sure that between 52% and 68% of adults in this sample will root for north high school.

Explanation:

A confidence interval gives a range of values within which we are a certain percentage (in this case 95%) confident that the True population parameter lies. Here, the parameter is the proportion of all adults in the city rooting for North High School.

• Option A is wrong because it misinterprets the confidence interval as a proportion over time.
• Option B has an incorrect upper - limit (68% is the upper - limit in the confidence interval, not 98%).
• Option D is wrong because the confidence interval is about the population (all adults in the city), not the sample.

Answer:

C. We are 95% sure that between 52% and 68% of all adults in this city will root for North High School.