Question

10. Show work when needed.A researcher wants to investigate the number of hours high school students spend doinghomework each night. After surveying 1,200 high school students, the researcher makes theclaim that she is 95% confident that the number of hours students spend doing homework eachnight is between 0.6 and 2.8 hours.a. What is the mean and margin of error for this confidence interval?

Answer 1

The z score for a 95% confidence level is 1.96

we then substitute the intervals and the z score to form two equations

$\begin{gathered} \bar{x}\text{ + z}\frac{s}{n}\text{ = 2.8 ----1} \\ \bar{x}\text{ - z}\frac{s}{n}\text{ = 0.6 ----2} \\ \text{Adding both equation,} \\ 2\bar{x}=3.4 \\ \text{Divide both side by 2} \\ \bar{x}\text{= 1.7} \\ \text{substituting the value of x in equation 1} \\ 1.7+\text{ z}\frac{s}{n}\text{ =2.8} \\ \text{ z}\frac{s}{n}=2.8-1.7 \\ \text{z}\frac{s}{n}=\text{ 1.1} \\ \\ \end{gathered}$

Therefore, the mean = 1.7

Margin of error = 1.1