Q:

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 "&lt;", "&gt;", "=", "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 =________

Accepted Solution

A:
Answer:p value = 0.3122Step-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 = 0.1667Pedro 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 =  0.4894p value = 0.3122p >0.05So not significant difference between the two proportions.