Question

students in a class were asked how many pets they had at home. their answers are below: 0,0,0,0,2,2,2,2,3,3,4,5,6,6,6,6,7,7,7,7,7,8,8,8,8. refer to the data above. what was the population mean of the number of pets living in students homes according to the pet survey? (4 points) 2. in a survey of 930 students in a school, 92% reported having pets at home. what is the margin of error? use the formula $pm\frac{1}{sqrt{n}}$ where n is the population. (4 points)

Explanation:

Step1: Calculate sum of data

$0\times4 + 2\times4+3\times2 + 4\times1+5\times1+6\times4+7\times5+8\times4=0 + 8+6 + 4+5+24+35+32 = 114$

Step2: Calculate number of data points

There are $4 + 4+2+1+1+4+5+4=25$ data - points.

Step3: Calculate population mean

The population mean $\mu=\frac{\sum x}{N}$, where $\sum x$ is the sum of data and $N$ is the number of data points. So $\mu=\frac{114}{25}=4.56$

Step4: Calculate margin of error for second - part

Given $n = 930$, using the formula $E=\pm\frac{1}{\sqrt{n}}$, we have $\sqrt{n}=\sqrt{930}\approx30.5$. Then $E=\pm\frac{1}{30.5}\approx\pm0.033$

Answer:

1. The population mean of the number of pets is $4.56$.
2. The margin of error is approximately $\pm0.033$.