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[null,null,null,"OBJECTIVE: Determining whether a coin is fair or not (Fair coin would be that there is equal prob of getting a head or a tail when I toss it)"]
[]
[null,"NULL HYPOTHESIS: Each coin is fair*"]
[]
[null,"Chosen Process: Toss each coin 10 times and count the total number of heads"]
[null,"(Number of heads will be called the test statistic because we will determine whether the coin is fair or not based on the number of heads)"]
[]
[null,"Steps for rejecting the NULL hypothesis (or in other words rejecting that the coin is fair):"]
[null,"Step 1: ","Determine the confidence interval (can be 95%, 90% etc.)**"]
[null,null,"What does the confidence interval mean?"]
[null,null,"In layman terms: How confident do we want to be about rejecting the coin?***"]
[null,null,"a) Say we want to be 99.5% confidence. We toss the coin 10 times and we get 9 heads."]
[null,null,"Now although it extremely unlikely that a fair coin will yield such a result but still there is a 1% prob. (see the table) for such an event to happen."]
[null,null,"Therefore, if we want to be 99.5% confident about our result we would not reject this coin (we will only reject it if we get 10 heads)"]
[null,null,"b) Say we want to be 95% confident. We toss the coin 10 times and again we get 9 heads."]
[null,null,"This time we will reject this coin because our confidence level is lower."]
[null,"Step2: ","Conduct the experiment"]
[null,null,"Note the test statistic. "]
[null,null,"If the probability of getting the test statistic is lower than (100%-confidence Interval), we reject the Null hypothesis"]
[null,null,"If our confidence interval is 95%, then we will reject the coin if the test-statistic that we get has a probability of less than 5% (100-95%)."]
[null,null,"For eg.: If our confidence interval was 95%, and the test statistic for a particular coin is 8. We will reject this coin."]
[null,null,"Because the probability of getting 8 heads is 4.4% which is lower than 5% (100%-95%)."]
[null,null,"This probability is actually the p-value.****"]
["We reject the NULL HYPOTHESIS only if the probability of getting that test-statistic is less than (100%-CI%)"]
[]
[null,null,null,"Number of heads",null,"Probability if the Null hypothesis is true"]
[null,null,null,null,0,{"$f":"COMBIN(10,E27)*(0.5^10)","v":9.765625E-4},null,null,"if my criteria was to reject the test statistic below 2.5%"]
[null,null,null,null,1,{"$f":"COMBIN(10,E28)*(0.5^10)","v":9.765625E-3},null,null,"I would reject coins that show a total of 0 or 1 or 9 or 10 heads after tossing 10 times"]
[null,null,null,null,2,4.39453125E-2]
[null,null,null,null,3,0.1171875]
[null,null,null,null,4,0.20507812499999997,null,null,"if my criteria was to reject the test statistic below 10%"]
[null,null,null,null,5,{"$f":"COMBIN(10,E32)*(0.5^10)","v":0.24609375},null,null,"I would reject coins that show a total of 0 or 1 or 2 or 8 or 9 or 10 heads after tossing 10 times"]
[null,null,null,null,6,0.20507812499999997]
[null,null,null,null,7,0.1171875]
[null,null,null,null,8,4.39453125E-2]
[null,null,null,null,9,9.765625E-3]
[null,null,null,null,10,9.765625E-4]
[]
[]
[]
[]
[]
["*PS: In statistics we want to reject the null hypothesis to accept the results as statistically significant."]
["**PS: 95% is my most common choice in all my strategies."]
["***PS: The actual interpretation of confidence interval is: It refers to the reliability of the estimation procedure."]
["****PS: The p-value is the probability of observing a value for our test statistic (that we have calculated from our sample data), given that the null hypothesis is true."]

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