SOLUTION: A coin is tossed 9 times and 3 heads appear. Can you conclude that the coin is not balanced? Use α = 0.10. Hint: Use the binomial table and ﬁnd 2P (X ≤ 3) with p

Question 974672: A coin is tossed 9 times and 3 heads appear. Can you conclude that the coin is not balanced? Use α = 0.10. Hint: Use the binomial table and ﬁnd 2P (X ≤ 3) with p = 0.5 and n= 9.
The answer shown is "No since p = 0.0508". However, I still don't understand how this answer is given because when I refer to binomial table (using n=9, p= 0.5 and X= 3), I got p = 0.164.
Can someone show me the step by step working solution? Truly appreciate that.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
First, I think about the problem and see what makes sense. With a 50% probability, the expected value is 4.5, and 3 would not be unusual.
alpha = 0.10, probability of rejecting Ho given that it is true.
P (0) given p=0.5 is 0.001953
P(1) is 0.0176
P(2) is 0.0703
P(3) is 0.1641
I get a probability of 0.2539, which makes me fail to reject the null hypothesis and makes sense to me.
The only way I see "508" is if the decimal place was mistaken and p=0.508. That would be doubling the p-value obtained. If I am doing a 2-tail test, then I would double the p-value. Otherwise, I would accept the p-value I obtained. My guess is that the p-value was doubled, and the decimal point was misplaced.

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SOLUTION: A coin is tossed 9 times and 3 heads appear. Can you conclude that the coin is not balanced? Use &#945; = 0.10. Hint: Use the binomial table and &#64257;nd 2P (X &#8804; 3) with p

SOLUTION: A coin is tossed 9 times and 3 heads appear. Can you conclude that the coin is not balanced? Use α = 0.10. Hint: Use the binomial table and ﬁnd 2P (X ≤ 3) with p