Question

Translate the statement into a confidence interval. Approximate the level of confidence. In a survey of 1043 adults in a country, 77% said being able to speak the language is at the core of national identity. The survey's margin of error is ±3.1%. The confidence interval for the proportion is (0). (Round to three decimal places as needed.)

Answer 1

To create a confidence interval for the proportion of American adults who believe the event is likely or very likely, use the plus-four method. A 97% confidence interval means that approximately 97% of the intervals would contain the true proportion of town residents who think winter-proofing their cars is very important.

Step-by-step explanation:

To create a confidence interval for the true proportion of American adults who believe that the event is likely or very likely, we can use the plus-four method. In this method, we add two successes and two failures to the original counts and calculate the proportion. For the given problem, 9 out of 48 respondents rated the event as likely or very likely. We add 2 to both the success count and the failure count, resulting in 11 out of 52. We can then calculate the confidence interval using this adjusted proportion, along with the sample size and the desired level of confidence.

A confidence interval is a range of values within which we can be confident that the true population proportion lies. In this context, a 97% confidence interval means that if we were to repeat the survey many times and construct a confidence interval each time, approximately 97% of these intervals would contain the true proportion of town residents who think winter-proofing their cars is very important.