Question

1. a sample of 125 households in a town near orange park reports an average of 2.3 children per household, with a margin of error of ±0.8. if the town has a total of 2,750 households, which is the estimated number of children living in the town?

a) between 2,750 and 6325
b) between 4,125 and 8,525
c) between 5,000 and 7,000
d) between 6,000 and 9,000

Explanation:

Step1: Calculate the lower bound

The formula for the confidence interval is \(\text{Lower Bound}=\text{Sample Mean}-\text{Margin of Error}\). The sample mean is \(2.3\) and the margin of error is \(0.8\). So, \(\text{Lower Bound}=2.3 - 0.8=1.5\). But wait, no! Wait, we need to consider the total number of households. The formula for the estimate of the population value is \(\text{Estimate}=n\times(\bar{x}\pm E)\), where \(n = 2750\), \(\bar{x}=2.3\), \(E = 0.8\). The lower bound of the estimate is \(n\times(\bar{x}-E)=2750\times(2.3 - 0.8)\)

$$2750\times1.5=4125$$

Step2: Calculate the upper bound

The upper bound of the estimate is \(n\times(\bar{x}+E)=2750\times(2.3 + 0.8)\)

$$2750\times3.1 = 8525$$

Answer:

B. Between \(4,125\) and \(8,525\)