Answer:
0.0253475; 0.0044944 ; 0.08809% ;(0.01654, 0.03416) ;
Explanation:
Given that:
n = 1223 ;
Yes = 31 ; No = 1192
a. Find the point estimate of the proportion of the population who were victims.
Yes / n = 31 / 1223 = 0.0253475
b. Find the standard error of this estimate.
Standard Error (se) :
Sqrt[(p(1 - p)) / n]
S. E= sqrt[(0.0253475(1 - 0.0253475)) / 1223]
S. E = √2.0200 * 10^-5
S.E = 0.0044944
c. Find the margin of error for a 95% confidence interval.
MOE = Zcritical * S. E
Zcritical at 95% = 1.96
MOE = 1.96 * 0.0044944
MOE = 0.008809024
MOE = 0.008809024 * 100%
MOE = 0.08809%
d. Construct the 95% confidence interval for the population proportion. Can you conclude that fewer than
10% of all adults in the United States were victims?
Confidence interval :
Mean ± MOE
0.0253475 ± 0.008809024
LOWER BOUNDARY :
0.0253475 - 0.008809024 = 0.016538476
UPPER BOUNDARY :
0.0253475 + 0.008809024 = 0.034156524
(0.01654, 0.03416)
Fewer than 10% of alduts are victims (10% = 0.1) ; interval values is less than 0.1
