1. ## Chi square Test

The Distribution of digits in numbers chosen at random from the telephone directory are:
Digit 0 1 2 3 4 5 6 7 8 9
Frequency 1026 1107 997 966 1075 933 1107 972 964 853
Test whether the digits may be taken to occur equally frequently in the directory
My problem is which test to chose and why? Though I think that I should use Chi-square test, I still can't confidently say why? If it is chi-square test, then I don't know how to calculate expected frequency, Is there any specific formula to calculate it?

2. I would use a $\displaystyle \chi^2$ test.

With

$\displaystyle
H_0: \text{The observed frequencies are consistent the expected frequencies}$

$\displaystyle
H_A: \text{The observed frequencies are not consistent the expected frequencies}$

Reject $\displaystyle H_0:$ if $\displaystyle \sum \frac{(0-E)^2}{E}>\chi^2_{\alpha , df}$

3. Originally Posted by roshanhero
If it is chi-square test, then I don't know how to calculate expected frequency, Is there any specific formula to calculate it?
For expected frequencies to occur evenly.

Sum these guys

Originally Posted by roshanhero
Frequency 1026 1107 997 966 1075 933 1107 972 964 853
And divide the result by 10. Allocate this new figure for each digit.

4. Thanks,but how to find the expected frequency when expected frequencies do not occur evenly.

5. Good question, this can be done but you need more (particular) information on how the expected frequencies are distributed unevenly.

The way around this is to test the data like in post #1. If you choose to reject the null hypothesis then you say there is evidence to suggest they are not distributed evenly.