Final answer:
To find the 98% confidence interval for the difference in the proportion of people that live in a city who identify as a 'dog person' and the proportion of people that live in a rural area who identify as a 'dog person' (p1 - p2), we can use the formula: CI = (p1 - p2) +/- Z * sqrt(p1 * (1-p1)/n1 + p2 * (1-p2)/n2). Substituting the given values, the confidence interval is (-0.1793, 0.1217).
Step-by-step explanation:
To find the 98% confidence interval for the difference in the proportion of people that live in a city who identify as a 'dog person' and the proportion of people that live in a rural area who identify as a 'dog person' (p1 - p2), we can use the formula:
CI = (p1 - p2) +/- Z * sqrt(p1 * (1-p1)/n1 + p2 * (1-p2)/n2)
Where:
p1 = proportion of city residents who identify as 'dog person'
p2 = proportion of rural residents who identify as 'dog person'
n1 = size of city sample
n2 = size of rural sample
From the given information:
p1 = 93/201 = 0.4627
p2 = 58/118 = 0.4915
n1 = 201
n2 = 118
Now we can substitute these values into the formula and calculate the confidence interval:
Z-score for a 98% confidence interval = 2.33
CI = (0.4627 - 0.4915) +/- 2.33 * sqrt(0.4627 * (1-0.4627)/201 + 0.4915 * (1-0.4915)/118)
CI = -0.0288 +/- 2.33 * sqrt(0.0019196 + 0.0022654)
CI = -0.0288 +/- 2.33 * sqrt(0.004185)
CI = -0.0288 +/- 2.33 * 0.0646
CI = -0.0288 +/- 0.1505
CI = (-0.1793, 0.1217)
Therefore, the 98% confidence interval for the difference in the proportion of people that live in a city who identify as a 'dog person' and the proportion of people that live in a rural area who identify as a 'dog person' is (-0.1793, 0.1217).