Question

centages 2 2) Test the claim that the given distribution agrees with agrees with the claimed per PA = 20% Po = 40% Po=40% Category (x=0.05) A 25 65 Frequency B С

please show work.

Answer 1

Hypothesis:

H₀ : Given distribution agrees with claimed percentage

H_a : Given distribution does not agree with claimed percentage.

Observation table:

Category	Frequency (Oi)	Prob. Pi	Expected freq (Ei)	(Oi-Ei)2/Ei
A	25	0.2	29	0.5517
B	55	0.4	58	0.1552
C	65	0.4	58	0.8448
	N = 145		145	1.5517

Expected frequency = N * Pi

Test statistic,

$\\ \chi ^2 = \sum \left [ \frac{(O_i-E_i)^2}{E_i} \right ] \\\\ \chi ^2 = 1.5517$

Degrees of freedom = n-s-k-1 = 3-0-0-1 = 2

Where,

n = Total number of observations

s = number of parameter estimated

k= number of degrees of freedom lost due to pooling

Critical value at 0.05 level of significance = 5.991

Since calculated test statistic is less than critical value hence we accept null hypothesis and conclude that given distribution agrees with claimed percentage at 5% level of significance.