An educational organization wants to estimate the number of high school seniors in a schoo… — SAT

An educational organization wants to estimate the number of high school seniors in a school district who plan to major in a STEM field. A random sample of $320$ high school seniors in the district was surveyed, and $35\%$ of the surveyed students reported that they plan to major in a STEM field. The survey has an associated margin of error of $4\%$ . There are $4,500$ high school seniors in the school district. Based on these results, what is the maximum estimated number of high school seniors in the district who plan to major in a STEM field?

Answer: 1755

Answer

1755

The survey estimate for the proportion of students who plan to major in a STEM field is

35\%

with a margin of error of

4\%

. This means the true proportion is estimated to be between

35\% - 4\% = 31\%

and

35\% + 4\% = 39\%

. To find the maximum estimated number of students in the population of

4,500

, we use the maximum estimated proportion of

39\%

(or

0.39

). Multiplying

0.39

4,500

yields

1,755

Step-by-Step Solution

Calculate the maximum estimated percentage of students by adding the margin of error to the sample percentage.

39\%

(or

0.39

)

The margin of error gives the range of values above and below the sample estimate that represents the true population proportion. The maximum value of this range is found by adding the margin of error.

Multiply the maximum estimated proportion by the total number of high school seniors in the district.

1,755

To generalize the sample results to the entire population of

4,500

seniors, multiply the maximum proportion by the total population size.

Key Concept

Estimating population parameters using sample proportions and margin of error

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