Question

Pedro thinks that he has a special relationship with the number 3. In particular, Pedro thinks that he would roll a 3 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 3.


(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 = 30 rolls, and a 3 comes up 6 times out of the 30 rolls. Determine the P-value of the test:

P-value =________

Answer 1

Answer:

p value = 0.3122

Step-by-step explanation:

Given that Pedro thinks that he has a special relationship with the number 3. In particular,

Normally for a die to show 3, probability p = $\frac{1}{6} =0.1667$

Or proportion p = 0.1667

Pedro claims that this probability is more than 0.1667

$H_0 = P =0.1667______H_a = P>0.1667_____$

where P is the sample proportion.

b) n=30 and $P = 6/30 =0.20$

Mean difference = $0.2-0.1667=0.0333$

Std error for proportion = $\sqrt{\frac{p(1-p)}{n} } \\=0.0681$

Test statistic Z = p difference/std error =  0.4894

p value = 0.3122

p >0.05

So not significant difference between the two proportions.