Pedro thinks that he has a special relationship with the number 1. In particular

Question

Pedro thinks that he has a special relationship with the number 1. In particular, Pedro thinks that he would roll a 1 with a fair 6-sided die more often than you'd expect by chance alone. Suppose p is the true proportion of the time Pedro will roll a 1.

(a) State the null and alternative hypotheses for testing Pedro's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "<", ">", "=", "not =" and express any values as a fraction e.g. p = 1/3)

H0 =

Ha =

(b) Now suppose Pedro makes n = 46 rolls, and a 1 comes up 10 times out of the 46 rolls.

Determine the P-value of the test: P-value =

Explanation / Answer

a)Ho: p=1/6

Ha: p>1/6

b) here mean =np=46*1/6=7.6667

std deviation =(np(1-p))1/2 =2.5276

therefore p value =P(X>=10) =1-P(X<=9)=1-P(Z<(9.5-7.6667)/2.5726)=1-P(Z<0.7253)=1-0.7659=0.2341

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