Question

4. In an experiment there were Nexp values measured. The expected values based on similar measurements are known. Both sets are presented in the Table of data. The question that arose was whether the differences between the observed and expected data are due to chance. Use the chi-square test to determine the probability that the differences arose from chance.

Data
Index	Observed	Expected
1	8.00	6.40
2	10.00	13.60
3	16.00	13.00
4	7.00	9.00
5	13.00	10.00
6	11.00	12.00
7	6.00	8.00
8	7.60	6.40
Nexp	8

Answer 1

Ho:there is no significant difference between the expected and observed result

H1:there is a significant difference between the expected and observed result

Index	Observed	Expected	(O-E)²/E
1	8	6.4	0.4
2	10	13.6	0.952941176
3	16	13	0.692307692
4	7	9	0.444444444
5	13	10	0.9
6	11	12	0.083333333
7	6	8	0.5
8	7.6	6.4	0.225
		total	4.1980266

chi square statistic = Σ(O-E)²/E=           4.198
          
degree of freedom = n-1 = 7          
          
p-value =    0.7567

p-value >α=0.05

so, there is no significant difference between the expected and observed result