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Komok [63]
3 years ago
15

February 12, 2009 marked the 200th anniversary of Charles Darwin's birth. To celebrate, Gallup, a national polling organization,

surveyed 1,018 randomly selected American adults about their education level and their beliefs about the theory of evolution. In their sample, 325 of their respondents had some college education and 228 were college graduates. Among the 325 respondents with some college education, 133 said that they believed in the theory of evolution. Among the 228 respondents who were college graduates, 121 said that they believed in the theory of evolution.
We want to test, at the 10% level, if there is evidence that the proportion of college graduates that believe in evolution differs significantly from the proportion of individuals with some college education that believe in evolution. Assume that the Pooled proportion (for standard error): = 0.459.
What is the z test statistic for this hypothesis test?
Mathematics
1 answer:
timurjin [86]3 years ago
5 0

Answer:

Z_{H0} = 2.83

Reject H₀

Step-by-step explanation:

Hello!

The objective of the poll is to compare the proportions of people who believe in the theory of evolution. For this, the investigator took a sample of 1018 and divided it into two groups using a criteria their level in college education.

Group 1 (people with some college education)

n₁= 325

x₁= 133

sample proportion ^ρ₁=x₁/n₁ = 133/325 = 0.409

Group 2 (college graduates)

n₂= 228

x₂= 121

sample proportion ^ρ₂=x₂/n₂ = 121/228 = 0.531

pooled proportion ^ρ= 0.459

The statistic test that corresponds to test if the proportions are equal or different is the difference of population proportions and you have to use the normal approximation for the proportions to calculate it.

The hypothesis is:

H₀: ρ₂=ρ₁

H₁: ρ₂≠ρ₁

α: 0.10

Z=<u>    (^ρ₂ - ^ρ₁) - (ρ₂ - ρ₁)   </u> ≈ N (0;1)

     √(^ρ(1 - ^ρ)*(1/n₂+1/n₁)

The critical region is  two-tailed, so you have a lower critrical value and an upper critical value:

Z_{\alpha /2} = Z_{0.05} = -1.64

Z_{1-\alpha /2} = Z_{0.95} = 1.64

If Z_{H0} ≤ -1.64 or if Z_{H0} ≥ 1.64 you reject the null hypothesis.

If -1.64 < Z_{H0} < 1.64, the you do not reject the null hypothesis.

Z=<u>    (^ρ₂ - ^ρ₁) - (ρ₂ - ρ₁)   </u> = <u>          (0.531 - 0.409) - 0         </u> = 2.83

     √(^ρ(1 - ^ρ)*(1/n₂+1/n₁)      √(0.459(1 - 0.459)*(1/228+1/325)  

Z_{H0} = 2.83

Since the calculated Z value is greater than the upper critical value, the decision is to reject the null hypothesis. In other words, there is significative enough evidence to say that there is a difference between the population proportion of people who believe in the evolution theory and graduated from college and the population proportion of people who believe in the evolution theory and have some college education.

I hope it helps!

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Let's let

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<u>y = the number of Caesar salads, y>=0</u>

The constrains are:

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The objective function here is F(x, y) = 0.75x + 1.20y

The corner points are (40, 35),  (60, 35), (60, 40), (50, 50) and (40, 50).

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3 years ago
Does anyone understand how to do this
Lerok [7]

Answer:

Step-by-step explanation:

I understand it!  (But I'm a high school math teacher so it might be unfair!) ; )

Anyway you have 2 numbers.  You don't know what they are so we will call them x and y.  Our first statement says that these numbers multiply to equal 120.  So that first equation is

xy = 120

Our second statement says that they add to -22.  So that second equation is

x + y = -22

Now we need to find the 2 numbers.  We have 2 unknowns, x and y.  That means that we have to have 2 equations.  No more than 2 no less than 2.  Solve the first equation for y.  It doesn't matter which equation you pick and which variable you choose to solve for.  If you do the work correctly, you will get the correct answers either way.  Solving the first equation for y gives you:

y=\frac{120}{x}

Now tht we have a value for y, we can use the substitution property of equality to sub that value into the second equation for y:

x+\frac{120}{x}=-22

Instead of finding a common denominator, we are going to eliminate x in the denominator altogether.  Do this by multiplying everything by x to get

x^2+120=-22x

Get everything on one side of the equals sign and factor:

x^2+22x+120=0

Because 12 * 10 = 120 and 12 + 10 = 22, our factors are 12 and 10:

x^2+12x+10x+120=0

Use factoring by grouping now.  

(x^2+12x)+(10x+120)=0

From the first set of parenthesis you can factor out an x, and from the second set you can factor out a 10:

x(x + 12) + 10(x + 12) = 0

Now factor out the common x + 12 to get a factored quadratic:

(x + 12)(x + 10) = 0

By the Zero Product Property, either x + 12 = 0 or x + 10 = 0.  Solving both for x gives you x = -12 or x = -10.

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y = -10

If x = -10, then

-10 + y = -22 so

y = -12.

The combinations of x and y are:

If x = -12, y = 10

If x = -10, y = -12

It doesn't matter which one is which.  They are not asking you to specifically define x and y.  They are asking you to find the numbers, and you did!

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