Question

You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:

HoHo : pA=0.4pA=0.4;  pB=0.1pB=0.1;  pC=0.2pC=0.2;  pD=0.3pD=0.3

Complete the table. Report all answers accurate to three decimal places.

Category	Observed Frequency	Expected Frequency	Residual
A	50
B	10
C	16
D	33

What is the chi-square test-statistic for this data?
χ2=χ2=

For significance level alpha 0.1, what is the chi-square Critical Value?
Critical Value =

What would be the conclusion of this hypothesis test?

• Fail to reject the Null Hypothesis
• Reject the Null Hypothesis

Answer 1

solution Given 1. Data The claim the following that the u categories occur with Srequencies. - Ho: PA :0.4, PB: 0.1, Pc: 0.2, PD: 0.3 Expected (p* Total) expected Probability Observed (6) category 0.9394 0.4 (109x0.4) - 13.6 0.0743 10.9 1.54311 21.8 32.7 0.0027 109 2.55951 (observed - Expected)? Expected 0.9394 (50 - 43.6) - 43.6 (6-4) 40.96 13.6 - 43.6 step : orto the chi-square test - stalistic is - 9,5 sº |

step o critical value at signibi cance level d=0.1 1 - H degree of freedom an- - 3 at df = 3 and significance level &= 0.1 at critical value is critical value = 11.345 step P value is = 0.0099 ( dt = 3, critical value = 11.345 and 2=0,01) (from - exitical value calculator) P. value is = 0.4647 [dt= 3, chi-square = 2.559, 2=0.01, from p-value chi-squcere calculator) 50 P value o significance level 0.01 so fail to reject Null hypothesis,