In a survey on student age and success, I am provided the information that 18% of the 8248 students at Madeup University are 25 years or older.

Approximately how many of the students in my sample should be 24 years or younger, to ensure a stratified sample?

Question

In a survey on student age and success, I am provided the information that 18% of the 8248 students at Madeup University are 25 years or older.

Approximately how many of the students in my sample should be 24 years or younger, to ensure a stratified sample?

BlackTom AI · Accepted Answer

We start by interpreting the problem: we have a total sample size of 8248 students, and 18% are 25 years or older.

Option-by-option analysis:

- 1485 students: This number corresponds to 18% of 8248 rounded to the nearest whole student (0.18 × 8248 ≈ 1484.64 ≈ 1485). If 1485 are 25 or older, the remaining younger students would be 8248 − 1485 = 6763. This would imply about 6763 students are 24 or younger, not 6764, so this option underestimates by one.

- 6764 students: This value aligns with the complement of the older group when rounding is applied. Since 82% (100% − 18%) should be 24 or younger, compute 0.82 × 8248 ≈ 6763.36, which rounds to about 6764 students. This matches the expected count for a stratified sample where the younger group is the remaining portion.

- 17 students: This is far too small to represent the 24-or-younger portion of the sample. It would imply an extremely disproportionate split and does not reflect the given 18% older share.

- 76 students: Similar to the previous option, this is far too small to represent the younger group in a sample of over 8,000, and it similarly ignores the 18% older proportion.

Putting it all together, the calculation that the younger group should comprise about 82% of the sample (since 18% are older) leads to 0.82 × 8248 ≈ 6763.36, which rounds to approximately 6764 students. The option that matches this estimate is the second one, 6764 students.

In a survey on student age and success, I am provided the information that 18% of the 8248 students at Madeup University are 25 years or older. Approximately how many of the students in my sample should be 24 years or younger, to ensure a stratified sample?

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