Question

In a survey of 23312331 ​adults, 730730 say they believe in UFOs. Construct a 99 %99% confidence interval for the population proportion of adults who believe in UFOs. A 9999​% confidence interval for the population proportion is ​(nothing​,nothing​). ​(Round to three decimal places as​ needed.) Interpret your results. Choose the correct answer below. A. With 9999​% ​probability, the population proportion of adults who do not believe in UFOs is between the endpoints of the given confidence interval. B. The endpoints of the given confidence interval shows that 9999​% of adults believe in UFOs. C. With 9999​% ​confidence, it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval. D. With 9999​% ​confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.

Answer 1

Answer:

0.288 < p < 0.338

Step-by-step explanation:

We have 2331 adults polled and 730 said they believe in UFOs.  We are to construct a 99% confidence interval for the population proportion.  We are told to round to 3 decimal places as needed.  

We need to find p-hat and q-hat

p-hat = 730/2331 = 0.313

q-hat = 1 - p-hat = 1 - 0.313 = 0.687

Since the sample size is greater than 30, we use a z-value for 99% confidence, which is 2.575

See attached photo for the construction of the confidence interval