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 di

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 =________

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Parker 2 weeks 2021-10-12T09:37:18+00:00 1 Answer 0

Answers ( )

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    2021-10-12T09:38:55+00:00

    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.

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