While working on your statistics HW in a local coffee shop, you are approached b

Question

While working on your statistics HW in a local coffee shop, you are approached by a stranger who puts a coin on the table and challenges you that the coin is fair. To test the stranger’s claim you start flipping the coin. Which of the following will provide the most convincing evidence that the stranger is trying to trick you and that the coin is actually not fair? You flip the coin 150 times and the coin shows ‘H’ in 96 out of the 150 flips. You flip the coin 25 times and the coin shows ‘H’ in 10 out of the 25 flips. You flip the coin 25 times and the coin shows ‘H’ in 15 out of the 25 flips. You flip the coin 150 times and the coin shows ‘H’ in 90 out of the 150 flips.

Explanation / Answer

here we use chi-square test and chi-squrare=sum((O-E)2/E)=9.88 with 3 df

with null hypothesis H0: observed frequency=expected frequency (coin is fair) and

alternate hypothesis H1: observed frequency is not equal to expected frequency(coin is not fair)

critical chi-square(0.05,3)=7.81 is less than calculated chi-square =9.88, so we fail to accept H0 and conclude that coin is not fair

there are k=4 classes , so here df=4-3

if coin is fair then expected frequency of Heand(H) will be half of the total frequency in each cases or classes

total Observed(O) Expected (E) (O-E) (O-E)2/E 150 96 75 21 5.88 25 10 12.5 -2.5 0.5 25 15 12.5 2.5 0.5 150 90 75 15 3 sum= 350 211 175 36 9.88

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