Question

a polling agency reported that the proportion of 12th grade students who are engaged is 0 34 engagement is defined as students involvement and enthusiasm with school the superintendent of one high school district believes the engagement of the districts students is higher than the proportion reported the district randomly surveys 90 of the 3600 students in the district and finds that 38 reported being engaged in school complete parts (a) through (e)
(a) what type of variable is \engaged\?
the variable is qualitative
(b) what is the sample proportion of students in this high school district who are engaged?
\\( \hat { p } = \square \\)
(round to four decimal places as needed )

Explanation:

Step1: Recall the formula for sample proportion

The formula for sample proportion $\hat{p}$ is $\hat{p}=\frac{x}{n}$, where $x$ is the number of successes (in this case, the number of engaged students) and $n$ is the sample size.

Step2: Identify the values of $x$ and $n$

Here, $x = 38$ (number of engaged students in the sample) and $n=90$ (sample size).

Step3: Calculate the sample proportion

Substitute the values into the formula: $\hat{p}=\frac{38}{90}\approx0.4222$

Answer:

$0.4222$