In a survey of 2340 adults, 750 say they believe in UFOs Construct a 95% confide

Question

In a survey of 2340 adults, 750 say they believe in UFOs Construct a 95% confidence interval for the population proportion of adults who believe in UFOs. A 95% confidence interval for the population proportion is (Round to three decimal places as needed.) Interpret your results. Choose the correct answer below. With 95% confidence, it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval With 95% probability, the population proportion of adults who do not believe in UFOs is between the endpoints of the given confidence interval. The endpoints of the given confidence interval shows that 95% of adults believe in UFOs. With 95% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.

Explanation / Answer

Confidence interval for population proportion is
sample proportion +/- confidence coefficient*standard error of p
Sampl eproportion = x/n = 750/2340 = 0.32
Confidence coefficient is the critical value of z for 95% confidence level = 1.96
Standard error of p = sqrt [p*(1-p)/n]
= sqrt [0.32*0.68/2340]
Therefore, the CI is
0.32 +/- 1.96 * sqrt [0.32*0.68/2340]
0.32 +/- 0.0189

0.32 +/- 0.02

lower bound is 0.32-0.02 = 0.30
upper bound is 0.32+0.02 = 0.34
The CI is (0.30, 0.34)

Option D:

with 95% confidence, it can be said that the population proportion of adults who believe in UFOs is between the end points of the given confidence interval

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