In 2011, a U. S. Census report determined that 68% of college students are working students. A researcher thinks this percentage has changed and surveys 144 college students. The researcher reports that 93 of the 144 are working students. Is there evidence to support the researcher's claim at the 1% significance level

We will fail to reject the null hypothesis and conclude that there is sufficient evidence not to support the researchers claim.

Step-by-step explanation:

We are given;

Population proportion; p = 68% = 0.68

Sample proportion; p^ = 93/144 = 0.6548

n = 144

The hypotheses are:

Null hypothesis;H0: p = 0.68

Alternative hypothesis;Ha: p ≠ 0.68

np = 144 × 0.6548 > 5 and nq = n(1 - p) = 144(1 - 0.68) > 5.

Since np and nq are more than 5, we can use the z-test .

z-formula in this case is;

z = (p^ - p)/√(p(1 - p))

Plugging in the relevant values, we have;

z = (0.6548 - 0.68)/√(0.68(1 - 0.6548))

z = -0.0252/0.4845

z = -0.052

From the z-table attached, we have a p-value of approximately 0.4801

P-value is higher than the significance level of 0.01.

Thus,we will fail to reject the null hypothesis and conclude that there is no sufficient evidence to support the researchers claim.

the input value is the number of times you fold it. the input value is also known as the x-value. 

the output value is its thickness. the output value is the y-value.

when you don't fold it all, the thickness will remain the same, which is 1. the ordered pair would be (0,1).

when you fold it once, the thickness will double from 1 to  2. the ordered pair would be (1,2).

when you fold it a second time, the thickness will double from 2 to  4. the ordered pair would be (2,4).

fold it one more time, and the thickness will be 8. the ordered pair is (3,8)

fold it the fourth time, and the thickness doubles. 8 x 2 = 16. the ordered pair is (4,16)

fold it the fifth time, and the thickness goes from 16 to 32. the ordered pair is (5,32)

the ordered pairs would be:

(0,1)

(1,2)

(2,4)

(3,8)

(4,16)

(5,32)

(6,64)

(7,128)

and so on : p

the question asks for 6 ordered pairs, so i bolded the first six.

now, the equation for this would be 

if we graph that, and we do the vertical line test, then we know this is a function.

it is a function because each x-value has a different y-value. there are no y-values that have the same x-values.

i have attached the graph of that line.

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step-by-step explanation: