3. in a survey of 850 students in a school, 90% reported having pets at home. if the margin of error is…

3. in a survey of 850 students in a school, 90% reported having pets at home. if the margin of error is ±3.4%, what is the interval that is likely to contain the exact percent of all people who have pets at home? (4 points)

3. in a survey of 850 students in a school, 90% reported having pets at home. if the margin of error is ±3.4%, what is the interval that is likely to contain the exact percent of all people who have pets at home? (4 points)

Answer

Explanation:

Step1: Identify the sample - proportion and margin of error

The sample - proportion $p$ is the percentage of students in the survey who reported having pets at home. Here, $p = 90%=0.9$, and the margin of error $E = 3.4% = 0.034$.

Step2: Calculate the lower limit of the confidence interval

The lower limit $L$ of the confidence interval is given by $L=p - E$. $L=0.9−0.034 = 0.866$ or $86.6%$.

Step3: Calculate the upper limit of the confidence interval

The upper limit $U$ of the confidence interval is given by $U=p + E$. $U=0.9 + 0.034=0.934$ or $93.4%$.

Answer:

The interval is $86.6%$ to $93.4%$.