Solutions of QUIZ 4. M262 Section 1. (04.04.2022).
1. From interviews with 1000 adults it was found that 780 adults supported tougher
legislation for antipollution measures. Does this poll substantiate the conjecture
that more than 75% of the adult population are in favor of tougher legislation for
antipollution measures? Use α = 0.1. Calculate the P-value.
Solution:
H0 : p = p0
H1 : p > p0
where p0 = 0.75.
Φ(zα ) = 1 − 0.1 = 0.9. Therefore, zα/2 = 1.28 and the rejection region is [1, 28, ∞).
p̂ − p 0.78 − 0.75
√ √0 = √ √ = 2.29 > 1.28
p̂q̂/ n 0.78 · 0.22/ 1000
Thus, we reject H0 and accept H1 .
Since Φ(2.29) = 0.9890 we find
P − value = P (Z ≥ 2.29) = 1 − Φ(2.29) = 0.011.
Note: Answers with P − value = P (Z ≤ 2.29) = 0.989 also will be accepted as
correct answers.
1
This study source was downloaded by 100000899606396 from CourseHero.com on 09-25-2025 13:19:15 GMT -05:00
https://www.coursehero.com/file/249824213/22262q4solpdf/
1. From interviews with 1000 adults it was found that 780 adults supported tougher
legislation for antipollution measures. Does this poll substantiate the conjecture
that more than 75% of the adult population are in favor of tougher legislation for
antipollution measures? Use α = 0.1. Calculate the P-value.
Solution:
H0 : p = p0
H1 : p > p0
where p0 = 0.75.
Φ(zα ) = 1 − 0.1 = 0.9. Therefore, zα/2 = 1.28 and the rejection region is [1, 28, ∞).
p̂ − p 0.78 − 0.75
√ √0 = √ √ = 2.29 > 1.28
p̂q̂/ n 0.78 · 0.22/ 1000
Thus, we reject H0 and accept H1 .
Since Φ(2.29) = 0.9890 we find
P − value = P (Z ≥ 2.29) = 1 − Φ(2.29) = 0.011.
Note: Answers with P − value = P (Z ≤ 2.29) = 0.989 also will be accepted as
correct answers.
1
This study source was downloaded by 100000899606396 from CourseHero.com on 09-25-2025 13:19:15 GMT -05:00
https://www.coursehero.com/file/249824213/22262q4solpdf/
