Question

For the following question:

a- Find the test statistic

b- Determine the p-value

c- Reject or fail to reject

Answer 1

We test this with chi-square goodness of fit test Null hypothesis: True proportions in all 4 categories is equal to their claimed value Alternative hypothesis: Atleast one proportions is different from its claimed value Ho : P1 = 0.52, = 0.38, P3 = 0.09, p4 = 0.01 Ha : Atleast one pi do not match the claimed value Expected Observed (O)(E -np) Expected # O- E)2 fraction (p) 0.52 0.38 0.09 0.01 470 498.68 364.42 86.31 9.59 1.649439 1 , 773 164 4.959751 116.395005 107 43 (O- E)2 -124.777359 Test statistic:124.78 Significance level - 0.05 Degrees of freedom ,df-k -1-3 To get p-value, we can use excel function CHÍSQ.DIST.RT( 124.777359 , 3) -7.2175x10-27 0.0000 p-value:0.0000 Since p-value is less than significance level α = 0.05 , we reject null hypothesis At 5% level, there is significant evidence that atleast one of the proportions differs from its claimed value