Question

9.1.5 The following sample of n = 20 s supposed to be from a Uniform(0, 1] distrib- ution 0.11 0.56 0.72 0.18 0.26 0.32 0.42 0.22 0.96 0.04 0.45 0.22 0.08 0.65 0.32 0.88 0.76 0.32 0.21 0.80 After grouping the data, using a partition of five equal-length intervals, carry out the chi-squared goodness of fit test to assess whether or not we have evidence against this assumption. Record the standardized residuals

Answer 1

Jiven hat n= 20 we nave the fellopi em te en data ols Tally bseyve expec 0 1 4 2253 02St 0.8-1 | 111 =g Total 20 20 3 O

. 13 27 Cal e. S-I te Lee on d vel n iconce. ata fit good to He uniborm. up post the assumplim H ence oun- 加own. evidence Nins stands dire hesidu! G-A)

for standardized residual (ti) follow the table below

		Table 2
fi	fe	(fi-fe)^2/fe	ei	fi-4	(fi-4)^2	V(ei)	hii	ti
4	4	0	0	0	0	0.8	0.666667	0
7	4	2.25	3	3	9	0.55	0.770833	2.611165
3	4	0.25	-1	-1	1	0.883333	0.631944	-0.6868
3	4	0.25	-1	-1	1	0.883333	0.631944	-0.6868
3	4	0.25	-1	-1	1	0.883333	0.631944	-0.6868
		3			12