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Ben has a coin which he claims is weighted in a way so that when he flips it, heads appears more often than 50% of the time. He tries to prove it to you by flipping the coin 100 times, which results in 60 heads.

Test the claim that the population proportion of heads that result from flipping this coin is actually more than 50%. Use a 1% level of significance.

Identify the sampling distribution you will use, what is the value of the test statistics, then find P-value.

I know the level of significance is 0.01; I'm just stuck on how to go about finding the null and alternate hypotheses. $\rm H_0$: would it be μ = 60, since that's the average of how many heads he got, and$\rm H_1: μ > 60$?

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  • $\begingroup$ We welcome questions like this, but we treat them differently. Please add the [self-study] tag & read this: stats.stackexchange.com/tags/self-study/info. Then tell us what you understand & have tried thus far, & where you are stuck, & we'll try to provide you hints to help get you unstuck. Note that just posting your homework & hoping someone will do it for you is grounds for closing. $\endgroup$ Jul 22, 2014 at 23:08
  • $\begingroup$ thank you! didn't know sorry , i've edited it. $\endgroup$
    – Jovany
    Jul 22, 2014 at 23:25
  • $\begingroup$ "would it be $μ$ = 60". No, your hypotheses do not come from your sample. What's the question you're trying to answer about the population mean? $\endgroup$
    – Glen_b
    Jul 23, 2014 at 3:51

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In hypothesis we always assume what you can think of as the uninteresting or default position than seek to find evidence against this suppositio (i.e. innocent until proven guilty; ps to better understand why we do this check out this video, https://www.youtube.com/watch?v=vKA4w2O61Xo&list=LL4aLT03KAOjLGpgETuW47dw&index=46) Our alternative hypothesis would just be our alternative belief about the situation. Now here we would assume the coin is fair (i.e. $H_{o}: \mu=0.5$, where $\mu$= average amount of heads in flips of coin) and seek to find evidence against this where our alternative hypothesis would be that it is biased towards heads so $H_{1}: \mu>0.5$ This alternative and null hypothesis can then be used to create the best test for this scenario

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    $\begingroup$ "In hypothesis [testing,] we always assume the opposite that we are trying to prove is correct and seek to show there is a lack of evidence towards such a supposition" Are you absolutely sure about this? $\endgroup$
    – jona
    Jul 23, 2014 at 0:06
  • $\begingroup$ Thanks for point that at Jona that is actually quite faulty of a statement. Didn't think that through when I wrote it very well, cause it could have been the situation for flipping coin that you want alternative to be $H_{1}:\mu=\frac{3}{4}$ where I guess opposite would $\mu\neq \frac{3}{4}$ which wouldn't want that to be your null hypothesis instead still would assume $\mu=\frac{1}{2}$ $\endgroup$
    – Kamster
    Jul 23, 2014 at 0:42
  • $\begingroup$ "Our alternative hypothesis would just be our alternative belief about the situatione". In my experience, this is not the view point shared in the literature see e.g. "When should we use one-tailed hypothesis testing?", onlinelibrary.wiley.com/doi/10.1111/j.2041-210X.2010.00014.x/… $\endgroup$
    – beuhbbb
    Jan 12, 2017 at 14:06

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