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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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Chloe and tino have a combined age of 48. three years ago chloe was double the age tino is now. find tinos age
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As  given Chole and Tinos age , the present age of Tino is equal to 15 years.

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Let x and y be the present age of Chole and Tino. respectively.

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Answer:

\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2}  t^2+1 \ \text{dt} \ = \ 2x^5-8x^2+2x-2

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\displaystyle{\frac{d}{dx} \int \limits_{2x}^{x^2}  t^2+1 \ \text{dt} = \ ?

We can use Part I of the Fundamental Theorem of Calculus:

  • \displaystyle\frac{d}{dx} \int\limits^x_a \text{f(t) dt = f(x)}

Since we have two functions as the limits of integration, we can use one of the properties of integrals; the additivity rule.

The Additivity Rule for Integrals states that:

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We can use this backward and break the integral into two parts. We can use any number for "b", but I will use 0 since it tends to make calculations simpler.

  • \displaystyle \frac{d}{dx} \int\limits^0_{2x} t^2+1 \text{ dt} \ + \ \frac{d}{dx} \int\limits^{x^2}_0 t^2+1 \text{ dt}

We want the variable to be the top limit of integration, so we can use the Order of Integration Rule to rewrite this.

The Order of Integration Rule states that:

  • \displaystyle\int\limits^b_a \text{f(t) dt}\  = -\int\limits^a_b \text{f(t) dt}

We can use this rule to our advantage by flipping the limits of integration on the first integral and adding a negative sign.

  • \displaystyle \frac{d}{dx} -\int\limits^{2x}_{0} t^2+1 \text{ dt} \ + \ \frac{d}{dx}  \int\limits^{x^2}_0 t^2+1 \text{ dt}  

Now we can take the derivative of the integrals by using the Fundamental Theorem of Calculus.

When taking the derivative of an integral, we can follow this notation:

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For the first term, replace \text{t} with 2x, and apply the chain rule to the function. Do the same for the second term; replace

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