Respuesta :
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
[tex][ p - 1.645\frac{\sqrt{pq} }{\sqrt{n}} ,p + 1.645\frac{\sqrt{pq} }{\sqrt{n}} ][/tex]
where 1.645 is Zac value at 90% confidence level.
[tex]p - 1.645\frac{\sqrt{pq} }{\sqrt{n}}[/tex] = 0.3187 - 0.0161 = 0.3026
[tex]p + 1.645\frac{\sqrt{pq} }{\sqrt{n}}[/tex] = 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 ]
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