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SAT Scores:

A college admissions officer sampled 126 entering freshmen and found that 45 of them scored more than 570 on the math SAT.

(a) Find a point estimate for the proportion of all entering freshmen at this college who scored more than 570 on the math SAT. Round the answer to at least three decimal places.

The point estimate for the proportion of all entering freshmen at this college who scored more than 570 on the math SAT is ___.

Answer :

To find a point estimate for the proportion of all entering freshmen at this college who scored more than 570 on the math SAT, we need to use the formula for the sample proportion.

The sample proportion [tex]\hat{p}[/tex] is calculated using the formula:

[tex]\hat{p} = \frac{x}{n}[/tex]

where:

  • [tex]x[/tex] is the number of successes in the sample (students who scored more than 570).
  • [tex]n[/tex] is the total number of observations in the sample.

Given in the problem:

  • [tex]x = 45[/tex] (students scored more than 570)
  • [tex]n = 126[/tex] (total students sampled)

Plug these values into the formula:

[tex]\hat{p} = \frac{45}{126}[/tex]

Calculate the proportion:

[tex]\hat{p} \approx 0.357[/tex]

So, the point estimate for the proportion of all entering freshmen at this college who scored more than 570 on the math SAT is approximately 0.357, rounded to three decimal places. This means about 35.7% of the entering freshmen in the sampled group scored more than 570 on the math SAT.

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