Chi-Square problems 1) Presume you have flipped a coin 6 times and got 4 heads a

Question

Chi-Square problems

1) Presume you have flipped a coin 6 times and got 4 heads and 2 tails. Is this an outcome equal to what you would expect?

2) Presume you flipped the coin 60 times and got the same frequency (40 heads, 20 tails). Is this outcome equal to what you would expect from flipping the coin 60 times? How does the probability compare with the results of the 6 flips?

3) Presume you flipped the coin 600 times and got the same frequency (400 heads, 200 tails). How does your test result compare with the first two results?

Explanation / Answer

Answer 1

Solution:

Here, we have flipped a coin about 6 times and we get the 4 heads and 2 tails. This outcome is not likely to what we expect. For the tossing of coin 6 times, we expect the 3 heads and 3 tails if the coin is unbiased. If the coin is unbiased then the probability of getting the head or tail at single draw is ½ = 0.5. Here, we do not get these probabilities for the outcomes.

So, for this scenario, the expected frequencies and observed frequencies are different.

Answer 2

Solution:

Here, we have flipped the coin about 60 times, and we get 40 heads and 20 tails. For this scenario, if the coin is unbiased we would expect the approximately 30 heads and 30 tails. For this experiment we get the same probabilities as we get in the first part such as probability for head as 40/60 = 4/6 = 2/3 and the probability for tail as 20/60 = 2/6 = 1/3 which is same as the first part.

So, for this scenario, the expected frequencies and observed frequencies are different.

Answer 3

Solution:

Here, we are given that the coin is tossed about 600 times and we get the 400 heads and 200 tails. For this scenario, the probability of getting the head is given as 400/600 = 4/6 = 2/3 and the probability for the tail is given as 200/600 = 2/6 = 1/3. This means, we get the same probability as in the first part and second part. The probabilities for the head and tail for the given three experiments are same however we expect the probabilities for head and tail as 0.5 for unbiased coin.

So, for this scenario, the expected frequencies and observed frequencies are different.

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