Question

A multinomial experiment produced the following results:

Category	1	2	3
Frequency	139	120	71

a.

Choose the appropriate alternative hypothesis at H₀: p₁ = 0.40, p₂ = 0.40, 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 at H0: p1 = 0.40, p2 = 0.40, and p3 = 0.20. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Test statistic

c.

Approximate the p-value.

	p-value < 0.005
	p-value > 0.100
	0.010 < p-value < 0.025
	0.025 < p-value < 0.050
	0.050 < p-value < 0.100

d.

At 10% significance level, can we reject H₀: p₁ = 0.40, p₂ = 0.40, and p₃ = 0.20?

	Yes since the p-value is less than α.
	Yes since the p-value is more than α.
	No since the p-value is less than α.
	No since the p-value is more than α.

Answer 1