STA1610
Assignment 5
Unique No:867182
Due 8 September 2025
, Question 1 — Goodness-of-fit (Chi-square)
Situation: Population proportions from ComputerWorld are taken as the expected
distribution:
Very satisfied 28%
Somewhat satisfied 46%
Neither 12%
Somewhat dissatisfied 10%
Very dissatisfied 4%
Sample (n = 500) observed counts:
Very satisfied: 105
Somewhat satisfied: 235
Neither: 55
Somewhat dissatisfied: 90
Very dissatisfied: 15
Expected counts (expected = proportion × 500): E = [140, 230, 60, 50, 20].
Compute chi-square statistic:
2
(𝑂𝑖 − 𝐸𝑖 )2
𝜒 =
𝐸𝑖
𝑖
Calculation (rounded):
𝜒 2 = 42.5254 Degrees of freedom 𝑑𝑓 = 𝑘 − 1 = 5 − 1 = 4 .
P-value: 𝑝 ≈ 1.30 × 10 −8 (very small).
Decision (α = 0.05): 𝑝 ≪ 0.05 → Reject the null hypothesis.
Assignment 5
Unique No:867182
Due 8 September 2025
, Question 1 — Goodness-of-fit (Chi-square)
Situation: Population proportions from ComputerWorld are taken as the expected
distribution:
Very satisfied 28%
Somewhat satisfied 46%
Neither 12%
Somewhat dissatisfied 10%
Very dissatisfied 4%
Sample (n = 500) observed counts:
Very satisfied: 105
Somewhat satisfied: 235
Neither: 55
Somewhat dissatisfied: 90
Very dissatisfied: 15
Expected counts (expected = proportion × 500): E = [140, 230, 60, 50, 20].
Compute chi-square statistic:
2
(𝑂𝑖 − 𝐸𝑖 )2
𝜒 =
𝐸𝑖
𝑖
Calculation (rounded):
𝜒 2 = 42.5254 Degrees of freedom 𝑑𝑓 = 𝑘 − 1 = 5 − 1 = 4 .
P-value: 𝑝 ≈ 1.30 × 10 −8 (very small).
Decision (α = 0.05): 𝑝 ≪ 0.05 → Reject the null hypothesis.
