Question

In a survey of 2264 adults, 729 say they believe in ufos. construct a 95 confidence interval for the population proportion of adults who believe in ufos.

Answer 1

90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the giver confidence interval [ 0.3026, 0.3348 ].

Here, we have given:

Number of adults (n) = 2272

Number of adults who believe in UFO (x) = 724

Sample proportion (p) = x/n

p = 724 / 2272

p = 0.3187

now, let q = 1 - p

q = 1 - 0.3187

q = 0.6813

Confidence level → 90%

The 90% confidence interval for population proportion is

$[ p - 1.645\frac{\sqrt{pq} }{\sqrt{n}} ,p + 1.645\frac{\sqrt{pq} }{\sqrt{n}} ]$

where 1.645 is Zac value at 90% confidence level.

$p - 1.645\frac{\sqrt{pq} }{\sqrt{n}}$  = 0.3187 - 0.0161 = 0.3026

$p + 1.645\frac{\sqrt{pq} }{\sqrt{n}}$ = 0.3187 + 0.0161 = 0.3348

90% confidence interval for the population proportion is

[ 0.3026, 0.3348 ]

Hence, With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the giver confidence interval [ 0.3026, 0.3348 ]

Learn more about " Population Proportion " from here: brainly.com/question/15087042

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