How random are your numbers? In this activity, find a friend, a family member or

Question

How random are your numbers?

In this activity, find a friend, a family member or a class mate and ask them to give you a list of 100 random digits (ranging from 0 to 9) from their head without the use of a calculator, computer or a printed random table numbers. (3 4 4 2 1 6 4 8 9 0 7 8 6 5 5 5 2 1 2 3 …. etc)

Then make a frequency table to determine how many times each digit is listed. (This will be your observed frequencies) You can use the following table for this purpose:

Now, let’s conduct a statistical test to determine if your friend’s random digits have a similar frequency distribution to what we would expect for true random digits. In other words, conduct a test to see if the Observed Frequencies make a “good enough fit” with Expected frequencies in the table above. If the frequencies are close to each other, then we can conclude that the digits were really random. Follow the following steps:

1. State the hypotheses:

H0:

H1:

2. What statistical test can be used here? Determine if the conditions of the test are satisfied.

3. Compute the test statistic and give your answer using the correct symbol. If you use your calculator, give your calculator command; if you use the formula, show your work.

Digits Observe Frequency Expected Frequency 0 9 10 1 9 10 2 10 10 3 11 10 4 12 10 5 5 10 6 7 10 7 11 10 8 12 10 9 14 10 Total 100 100

Explanation / Answer

1

H0: The exected frequencies are a good fit

H1: the expected freqeuncies are not a good fit

2) We use chi square test here. The conditions are

each expected frequency should be atleast 5.

the total number of values should be atleast 50.

the values should be independent of each other.

All these conditions are satisified by the data.

3. Excel is used to compute the test statisitc.

p value is 0.7197>0.05, hence H0 is accepted and we conclude that the expected frquencies are a good fit.

Goodness of Fit Test observed expected O - E (O - E)² / E % of chisq 9 10.000 -1.000 0.100 1.61 9 10.000 -1.000 0.100 1.61 10 10.000 0.000 0.000 0.00 11 10.000 1.000 0.100 1.61 12 10.000 2.000 0.400 6.45 5 10.000 -5.000 2.500 40.32 7 10.000 -3.000 0.900 14.52 11 10.000 1.000 0.100 1.61 12 10.000 2.000 0.400 6.45 14 10.000 4.000 1.600 25.81 100 100.000 0.000 6.200 100.00 6.20 chi-square 9 df .7197 p-value

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