Lacking a table of random numbers Dan decided to use the la

. Lacking a table of random numbers, Dan decided to use the last digits in a set of five-place tables of logarithms. The number of times each integer occurred in a sample of size n = 50 is given below. If the collection of last digits is random, then we would expect each integer to occur, on average, equally often.

Integer   0   1   2   3   4   5   6   7   8   9
Frequency   8   6   7   3   5   7   1   4   6   3

Do the observed frequencies meet this expectation? Perform the appropriate test and report your findings. Be sure to include all the necessary steps.

Solution

Lacking a table of random numbers, Dan decided to use the last digits in a set of five-place tables of logarithms. The number of times each integer occurred in a sample of size n = 50 is given below. If the collection of last digits is random, then we would expect each integer to occur, on average, equally often.

Integer   0   1   2   3   4   5   6   7   8   9
Frequency   8   6   7   3   5   7   1   4   6   3

Do the observed frequencies meet this expectation? Perform the appropriate test and report your findings. Be sure to include all the necessary steps.

Null hypothesis: each integer to occur on average equally

Alternate hypothesis: each integer to occur on average not equally

Goodness of Fit Test

observed

expected

O - E

(O - E)