To address the problem given, let's break down the required steps and the solutions in detail:
1. Identify the Population Parameter:
- The population parameter we are interested in is the proportion of students in the population that identify as Hispanic/Latino.
2. Find the Point Estimate for the Population Proportion:
- The point estimate [tex]\( \hat{p} \)[/tex] is the proportion of the sample that identifies as Hispanic/Latino.
- Given the sample size [tex]\( n = 350 \)[/tex] and the number of Hispanic/Latino students [tex]\( x = 63 \)[/tex], the point estimate [tex]\( \hat{p} \)[/tex] is calculated as:
[tex]\[
\hat{p} = \frac{x}{n} = \frac{63}{350} = 0.18
\][/tex]
3. Construct the Confidence Interval:
- The confidence interval provides a range within which we can be confident that the true population proportion lies.
- The margin of error (MOE) is given as 0.034.
To find the confidence interval, we use the formula:
[tex]\[
\text{Confidence Interval} = (\hat{p} - \text{MOE}, \hat{p} + \text{MOE})
\][/tex]
Plugging in the values:
[tex]\[
\text{Lower Bound} = 0.18 - 0.034 = 0.146
\][/tex]
[tex]\[
\text{Upper Bound} = 0.18 + 0.034 = 0.214
\][/tex]
Thus, the confidence interval is:
[tex]\[
(0.146, 0.214)
\][/tex]
4. State the Final Insight:
- The data suggests that with 90% confidence, the proportion of students that identify as Hispanic/Latino is between 0.146 and 0.214.
Summarizing:
- The point estimate [tex]\( \hat{p} \)[/tex] for the population proportion is [tex]\( 0.18 \)[/tex].
- The 90% confidence interval for the population proportion is [tex]\( (0.146, 0.214) \)[/tex].
