Pedro thinks that he has a special relationship with the number 5. In particular

Question

Pedro thinks that he has a special relationship with the number 5. In particular, Pedro thinks that he would roll a 5 with a fair 6-sided die more often than you'd expect by chance alone. Suppose pp is the true proportion of the time Pedro will roll a 5. (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) H0H0 = HaHa = (b) Now suppose Pedro makes n = 42 rolls, and a 5 comes up 9 times out of the 42 rolls. Determine the P-value of the test: P-value =

Explanation / Answer

a. By chance p=1/6, so we have to test null hypothesis

H0: p=1/6

With an alternative

H1:p>1/6

b. Let X denote the number of times 5 comes up, then X follows Binomial distribution with n=42 and p=1/6

We have X=9, so

p-value=P(X>9)

=1-P(X<=9)

=1- 0.8498 using excel function =binomdist(9,42,1/6,true)

=0.1502

As p-value>0.05, we do not reject null hypothesis and conclude that Pedro claim() is not supported.

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