Question : In 200 tosses of a coin, 115 heads and 85 tails were observed. Test the hypothesis that the coin is fair , using significance level 0.05
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Should i check for mean or should i check for variance
If you are going to be testing the mean, then you need to test with a null hypothesis of X equal to 100, and an alternate hypothesis of X not equal to 100.
The hypothesis you have set up now, is saying that this "fair coin" observance comes from a population with a mean of 85 tails. . .that doesn't make any sense. You are testing under the assumption that coin IS fair, and that this collection of 200 tosses you have sampled comes from a population of "coin tosses" with a mean of 100 tails and 100 heads.
When you are running your hypothesis test, you are essentially trying to figure out what are the chances that you grabbed one of the samples of 200 that have such an unbalanced distribution of heads and tails (assuming the coin is fair). If the probability is low (your p-value), or if its just lower than your significance level, then there might be good evidence that the sample you pulled from isn't one with an even distribution of heads and tails.
If the hypothesis that the coin is fair is to be tested, then
. The test will be two-tailed.
All the ideas necessary to answer the question are now in this thread.
The trouble is not that help is needed with this question (which is similar to some otheres that have previously been posted). The trouble is that all this material has to be presented and taught from scratch. MHF cannot do this. That is the job of the instructor, classnotes and textbook.
You should realise that the two formulae are equivalent. There are just notational differences. If you multiply the numerator and denominator of the formula quoted by Ond you get the formula quoted by yourself, aside from the notational differences.
You should also realise that:
1. and are the same thing (just different notation).
2. The estimator of is .
3. ~ Normal .
Your formula follows directly from this.
I have said this before: It is important to understand where a formula comes from and exactly what the symbols in it mean.