Solution:
Formula for calculation of 99% confidence interval is given by:
= [tex]P \pm (\text{Z value} )\sqrt\frac {P\times(1-P)}{N}[/tex]
P= Sample Proportion
N =Sample Size
Also,Number of voters who vote online= 19 % of 1300=19 × 13=247
Sample Population= [tex]=\frac{247}{1300}[/tex]=0.19
Z value for 99% confidence interval=2.58
The number of voters who vote online, who are in the 99% confidence interval for the percent of all voters who would prefer to vote online= [tex]0.19 \pm (2.58)\sqrt\frac{0.19 \times (1-0.19)}{1300}\\\\ =0.19 + (2.58)\sqrt\frac{0.19 \times (1-0.19)}{1300} {\text{or}} 0.19 - (2.58)\sqrt\frac{0.19 \times (1-0.19)}{1300}\\\\ 0.2180 {\text{or}} 0.1619[/tex]
So, Percent of voters , who are in the 99% confidence interval for the percent of all voters who would prefer to vote online= 100 × 0.2180 or 100 × 0.1619=21.80 % or 16.19 %
That is between, 16.19 % and 21.80 %.
→→Option (A) 19.8 % and Option (B)17.4 % are in 99 % confidence intervals.
