Question

in a survey of 2290 adults, 717 say they believe in UFO's

construct a 99% confidence interval for the population proportion of adults who believe in UFOS

a 99% confidence level for the population proportion is ( , ) round to three decimals.

interpret your results. Choose correct answer below.

A. with 99% probability the population proportion of adults who do not believe in UFOS is between the endpoints of the given confidence interval.

B. with 99% confidence it can be said that the population proportion of adults who believe in UFOS is between the endpoints of the given confidence interval.

C. the endpoints of the given confidence interval shows that 99% of adults believe in UFOs

D. with 99% confidence , it can be said that the sample proportion of adults who believe in UFOS is between the endpoints of the given confidence interval.

Answer 1

Solution :

n = 2290

x = 717

= x / n = 717 / 2290 = 0.313

1 - = 1 - 0.313 = 0.687

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.576 * (((0.313 * 0.687) / 2290 )

= 0.025

A 99 % confidence interval for population proportion p is ,

- E < P < + E

0.313 - 0.025 < p < 0.313 + 0.025

0.288< p < 0.338

Option D ) is correct.

D. with 99% confidence , it can be said that the sample proportion of adults who believe in UFOS is between the endpoints of the given confidence interval.