Question

Q10. A sample of 200 urban adult residents of Madina revealed 60 who favoured increasing the highway speed limit from 50 to 80km/hr, where as a sample of 160 rural residents yielded 68 favored the increase. Does this data indicate that the sentiment groups of residents? Test verses Using ∝ = 0.05, where P1 refers to the Urban population. P2 refers to rural population.                                                                                               [7 marks]

Answer 1

Hypothesis:

H₀: p₁ = p₂

H₁ : p₁ p₂

Sample size = n₁ = 200

p₁ = x₁ / n₁ = 60 / 200 = 0.3

Sample size = n₂ = 160

p₂ = x₂ / n₂ = 68 /160 = 0.425

p = (x₁ + x₂) / (n₁ + n₂)

= (60 +68) / (200 + 160)

= 0.3555

q = 1 - p

= 1 - 0.3555

= 0.6445

Test statistic

Z = -0.125 / 0.0508

Z = -2.46

At = 0.05

Z_crit = 1.96

At Z = -2.46

P- value = 0.00695

P - value <

0.00695 < 0.05 reject the null hypothesis.

There is sufficient evidence to conclude that the proportions are different.

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