Answer :
To find a point estimate for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT, we can use the formula for the sample proportion.
The sample proportion [tex]\hat{p}[/tex] is calculated by dividing the number of successes by the total number of observations in the sample.
Given:
- Number of freshmen who scored more than 590: 45
- Total number of entering freshmen sampled: 116
The formula for the sample proportion is:
[tex]\hat{p} = \frac{x}{n}[/tex]
Where:
- [tex]x[/tex] is the number of successes
- [tex]n[/tex] is the total number of observations
Substitute the given values:
[tex]\hat{p} = \frac{45}{116}[/tex]
Now, calculate the value:
[tex]\hat{p} = 0.38879[/tex]
Rounding this to three decimal places, the point estimate for the proportion of all entering freshmen at this college who scored more than 590 on the math SAT is:
[tex]\hat{p} = 0.389[/tex]
Therefore, the point estimate for the proportion is approximately 0.389.
