A multinomial experiment produced the following results Calc

A multinomial experiment produced the following results:

Calculate the value of the test statistic at H₀: p₁ = 0.58, p₂ = 0.27, and p₃ = 0.15. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Category	1	2	3
Frequency	180	66	54

A multinomial experiment produced the following results: Category 1 2 3 Frequency 180 66 54 a. Choose the appropriate alternative hypothesis at H0: p1 = 0.58, p2 = 0.27, and p3 = 0.15. HA: At least one of the pi(i = 1, 2, 3) is less from its hypothesized value. HA: At least one of the pi(i = 1, 2, 3) is more from its hypothesized value. HA: At least one of the pi(i = 1, 2, 3) differs from its hypothesized value. b. Calculate the value of the test statistic at H0: p1 = 0.58, p2 = 0.27, and p3 = 0.15. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Test statistic c. Approximate the p-value. p-value 0.100 0.025

Solution

(a) H_A: At least one of the p_i(i = 1, 2, 3) differs from its hypothesized value.

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(b)

observed

expected

O - E

(O - E)