Question

2) 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 = 42 rolls, and a 1 comes up 9 times out of the 42 rolls. Determine the P-value of the test:

P-value =

(c) Answer the question: Does this sample provide evidence at the 5 percent level that Pedro rolls a 1 more often than you'd expect? (Type: Yes or No)

Answer 1

GIVEN THAT :-

According to the question we have that ,

roll a 6 with a fair 6-sided die more often than you'd expect by chance alone.

time Pedro will roll a 6.

TO FIND:-a) State the null and alternative hypotheses for testing Pedro's claim.

we have that the answer the values for the H0 and Ha.

H0: p = 1/6 Ha: p ≠ 1/6

TO FIND:-b) Determine the P-value of the test:
first find the test statistic.

formula for Test statistic:-

Z = (p̂ - p)/sqrt(pq/n)

there fore we have Z value as

Z = 0.6136

since we have the values as:-

x =7 ;  n =34 ; p = 1/6 = 0.166667 ;

q = 1 - p = 0.833333 (pvalue = 0.6136)

TO FIND :-c)Does this sample provide evidence at the 5 percent level that Pedro rolls a 6 more often than you'd expect?

now

P-value is greater than alpha value 0.05, so we do not reject the null hypothesis.  

there fore NO

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