[R] One-sample test for p

Peter Dalgaard p.dalgaard at biostat.ku.dk
Thu Oct 16 13:35:25 CEST 2008

rr400 wrote:
> Hi, i am doing a statistics course and am having trouble with an exercise
> where i need to determine whether my success rate at something is higher
> than 80%. 
> I was successful in 29 out of 60 trials, so these were the commands i
> entered into R:
>> n=60
>> p.hat=29/n
>> p.0=0.8
>> se.0=sqrt(p.0*(1-p.0)/n)
>> z=(p.hat-p.0)/se.0
>> print(z)
> Which returned:
> [1] -6.132224
>> 1-pnorm(z)
> Which returned
> [1] 1
> My problem is that i am meant to state a null and alternative hypothesis
> which at the moment i have stated as  p>0.8 (null) and p≤0.8 (alternative).
> As things stand, though, a p-value of 1 suggests i should reject the null
> hypothesis which can't be right since i am obviously successful less than
> 80% of the time. 
> I am not sure where i am getting muddled. Any advice would be greatly
> appreciated. Thanks!

This isn't really about R, and maybe it is homework, but now that we got 
you in the appropriate frame of mind:

(a) p values should look at "this or more unfavourable" events. You have 
arranged things so that that translates to -6.13 or _lower_. I.e. you're 
looking at the wrong tail.

(b) Make sure you get your accept/reject logic right. You _reject_ the 
null when data would be _un_likely if the null hypothesis were true.

(c) You might also want to play with binom.test and prop.test

    O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
   c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
  (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45) 35327907

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