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Phantasy [73]
3 years ago
10

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

r 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 =________
Mathematics
1 answer:
anyanavicka [17]3 years ago
7 0

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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The length of a rectangle 8 more than the width .the area is 513 square inches .find the length and width of the rectangle
Pani-rosa [81]

Answer:

width =19 inches

length= 27 inches

Step-by-step explanation:

Let width be w inches so according to given scenario as length is 8 more than width so the equation becomes

l=8+w inches (Equation 1)

Area of Rectangle= L*w

Area= 513

L*w=513    (Equation 2)

Putting l's value from equation 1 in equation 2

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w^2+8w-513=0

Making Factors

w^2+27w-19w-513=0

w(w+27)-19(w+27)=0

(w-19)(w+27)=0

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as width cannot be negative so if we only consider w=19 then

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l=27

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