MATHEMATICS COLLEGE

Suppose that you are examining the difference in ages between brides and grooms. You are interested in conducting a significance test to examine to address the theory that the bride is younger than the groom in more than half of all marriages. A sample of 100 couples were observed, for which 67 had a bride younger than the groom.whats is the parameter? .
Step 2: The null hypothesis and alternative hypothesis?
Step 5: whats the p-value is:

Answers

Answer 1

Answer:

Parameter = 0.5

Null hypothesis : H0 : P0 = 0.5

Alternative hypothesis ; H0 : P0 > 0.5

Pvalue = 0.99966

Step-by-step explanation:

The parameter defines a statistical value or calculation which is derived from the population.

The parameter in this scenario is the population proportion, P0 which is 0.5

The scenario above describes a scenario to test the difference in population.

The null hypothesis, that bride and groom are of the same age ;

H0 : P0 = 0.5

The alternative hypothesis ; the bride is younger Than the groom in more than half of the population.

H1 : p0 > 0.5

To obtain the Pvalue :

Test statistic : (phat - P0) ÷ √(p0(1 -p0) / n)

Phat = x/n

x = 67 ; sample size, n = 100

Phat = x / n = 67/100 = 0.67

P0 = 1 - 0.5 = 0.5

Tstatistic = (0.67-0.50) ÷ √(0.5(0.5) / 100)

Tstatiatic = 0.17 ÷ 0.05

Tstatistic = 3.4

P-value : p(Z < 3.4) = 0.99966 (Z probability calculator).

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Use any method to multiply (-14ab)(a + 3b - 4c).

Answers

Answer:

-14a^2b-42ab^2+56abc

Step-by-step explanation:

You can use the FOIL method

multiply the first numbers

then inner

then outer

then last

Which is the best way to describe 1-2 ?-3
-2
-1
0
1
2
3
point A
the distance between A and D
the opposite of 2
the distance between A and C

Answers

Answer:

the distance between a and c.

Step-by-step explanation:

the absolute value of -2 is 2, and the distance between a and c is the only option that gives you a value of 2.

a 12-foot piece of string is cut into two pieces so that the longer piece is 3 feet longer than twice the shorter piece. find the length of both pieces. what is the length of the shorter piece

Answers

The longer piece would be 7.5f and the shorter 4.5

Evaluate the indefinite integral as a power series f(x) = 1 tan-1(x7) dx n=0 What is the radius of convergence R? R= -/0.77 points
Evaluate the indefinite integral as a power series x7 In(1 x) dx f(x) = C + n=0
What is the radius of convergence R?

Answers

Answer:

$\mathbf{f(x)=C + \sum \limits ^(\infty)_(n=0) ((-1)^n \ x^(14n +8))/((2n+1)(14n+8))}$

For convergence since |x| > 1

The radius of convergence R = 1

$\mathbf{f(x) = C + \sum \limits ^(\infty)_(n =0) \frac{(-1)^n \ x^(n+9)} {(n+1) (x^(n+9))}}$

For convergence since |x| < 1

The radius of convergence R = 1

Step-by-step explanation:

Given that:

$f(x) = \int tan^(-1) (x^7) \ dx$

Let recall that for Power series of tan⁻¹ (x)

$tan^(-1) (x) = \sum \limits ^(\infty)_(n=0) ((-1)^n x^(2n+1))/((2n+1))$

Then $tan^(-1) (x^7) = \sum \limits ^(\infty)_(n=0) ((-1)^n (x^7)^(2n+1))/((2n+1))$

$tan^(-1) (x^7) = \sum \limits ^(\infty)_(n=0) ((-1)^n \ x^(14n+7))/((2n+1))$

Thus;

$f(x) =\int tan^(-1) (x^7) \ dx = \int \sum \limits ^(\infty)_(n=0) ((-1)^n \ x^(14n+7))/((2n+1))$

$\implies \sum \limits ^(\infty)_(n=0) ((-1)^n )/((2n+1)) \int x^(14n+7) \ dx$

$\mathbf{f(x)=C + \sum \limits ^(\infty)_(n=0) ((-1)^n \ x^(14n +8))/((2n+1)(14n+8))}$

For convergence since |x| > 1

The radius of convergence R = 1

$\int x^7 \ In (1 + x) \ dx$

Recall that for power series of,

$In(1+x) = \sum \limits ^(\infty)_(n = 0) ((-1)^n \ x^(n+1))/(n +1)$

Thus;

$x^7 \ In (1+x) = x^7 \sum \limits ^(\infty)_(n =0) ((-1)^n \ x^(n+1) )/(n+1)$

$\implies \sum \limits ^(\infty)_(n =0) ((-1)^n \ x^(n+8) )/(n+1)$

$f(x) = \int x^7 \ In (1+x) \ dx = \int \sum \limits ^(\infty)_(n =0) ((-1)^n \ x^(n+8) )/(n+1) \ dx$

$=\sum \limits ^(\infty)_(n =0) ((-1)^n)/(n+1) \int \ x^(n+8) \ dx$

$\mathbf{f(x) = C + \sum \limits ^(\infty)_(n =0) \frac{(-1)^n \ x^(n+9)} {(n+1) (x^(n+9))}}$

For convergence since |x| < 1

The radius of convergence R = 1

Final answer:

To evaluate the indefinite integral as a power series for the given equations, we use the power series expansions of the functions involved. The radius of convergence, R, is the distance from the center of the power series to the nearest point where the power series diverges.

Explanation:

To evaluate the indefinite integral f(x) = 1/tan-1(x7) dx as a power series, we can use the power series expansion of tan-1(x). The power series expansion of tan-1(x) is x - (x3/3) + (x5/5) - (x7/7) + .... We substitute x7 for x in the power series expansion and integrate term by term. The radius of convergence, R, is the distance from the center of the power series to the nearest point where the power series diverges.

To evaluate the indefinite integral f(x) = x7ln(1-x) dx as a power series, we can use the power series expansion of ln(1-x). The power series expansion of ln(1-x) is -x - (x2/2) - (x3/3) - (x4/4) - .... We substitute x7 for x in the power series expansion and integrate term by term. The radius of convergence, R, is the distance from the center of the power series to the nearest point where the power series diverges.