Sampling Distributions for Sample Proportions

AP Statistics· difficulty 3/5

Researchers sample n = 25 from a city of 100,000 to estimate the proportion p with a hobby. Suppose p = 0.20.

Conditions Check np = 25(0.20) = 5 n(1-p) = 20 5 < 10 → fails

Are the conditions for approximate normality of p̂ satisfied?

  • A

    No, because n(1-p) > 10.

  • B

    No, because np = 5 < 10.

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  • C

    Yes, because n < 0.10·100,000.

  • D

    Yes, because n > 20.

Explanation

np = 25(0.20) = 5 < 10, so Large Counts fails.

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