Chi-squared question chapter 12 homework. Help please.

Question

You are conducting a multinomial hypothesis test for the claim that all 5 categories are equally likely to be selected. Complete the table.

Catagories Observed Freq. Expected freq. ² Person Residual

A 12

B 19

C 21

D 5

E 24

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

Report all answers accurately to three decimal places.

Answer 1

The total observed frequencies are 81

If all are equally likely then we would expect 81/5 = 16.2 in each category

Test statistic = sum of (observed - expected)² / expected for the five categories

So (1/16.2) [ (12-16.2)² + (19-16.2)² + (21-16.2)² + (5-16.2)² + (24-16.2)²]

You can calculate this

Can also do on a TI-84. Enter the observed in L1, expected in L2, then stat tests D (chi squared goodnes s of fit test). Put L1 and L2 with df = 4 (5-1).