Question

A multinomial experiment produced the following results: (You may find it useful to reference the appropriate table: chi-square table or F table)

Category	1	2	3
Frequency	117	100	83

a. Choose the appropriate alternative hypothesis at H₀: p₁ = 0.50, p₂ = 0.30, and p₃ = 0.20.

• All population proportions differ from their hypothesized values.

• At least one of the population proportions differs from its hypothesized value.

b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

c. Find the p-value.

• p-value < 0.01

• p-value 0.10
• 0.05 p-value < 0.10
• 0.025 p-value < 0.05
• 0.01 p-value < 0.025

d. At 1% significance level, can we reject H₀: p₁ = 0.50, p₂ = 0.30, and p₃ = 0.20?

• No since the p-value is more than significance level.
• Yes , since the p-value is more than significance level.
• No since the p-value is less than significance level.
• Yes since the p-value is less than significance level.

Answer 1

Solution:

a. Choose the appropriate alternative hypothesis at H₀: p₁ = 0.50, p₂ = 0.30, and p₃ = 0.20.

Answer: At least one of the population proportions differs from its hypothesized value.

b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Answer: 17.188

Explanation:

Category Frequency 117 100 83 Proportion 0.5 0.3 0.2 Expected 150 90 (0-E) E 7.26 1.111 8.817 wN 60 (0-E) = 17.188 Total 300 300 Σ Ε.

c. Find the p-value.

Answer: p-value < 0.01

d. At 1% significance level, can we reject H₀: p₁ = 0.50, p₂ = 0.30, and p₃ = 0.20?

Yes since the p-value is less than the significance level.