I am working on sample size of 70 . My observed and expected values are different (Observed 586, 648, 526, 662, 658, 502, ..... so on for 70 samples and expected 570 634, 513, 647, 644, 490, .....so on for 70 samples). I used Chi-sq test to check the null that there is no difference in observed and expected value. And I got a p-value of 0.99 which means I can't reject null. Can I use any other test for this kind of problem since I can see that for all the 70 samples observed is higher than expected but I cant show this result statistically.
Sounds like you need a paired t-test (which will use the difference between each observed and actual observation), or a non-parametric equivalent (which would pick up on the fact that more of the observed numbers are larger than expected than would be expected if it were a 50-50 chance).
To be fancy you could adjust for the fact that the observations are counts and hence unlikely to be normally distributed. This would require, for example, a model whereby each observation has a poisson distribution and hence the variance increases as the mean increases. In practice, if your example data reflects the overall set, you will get a similar result to a paired t-test.