Mathematics College

In 2020 researchers took random samples to compare the proportion of adult females to the proportion of adult males who use 2 or more credit/debit cards. The adults were aged 21 and older and they lived in all areas of the U.S. Based on the data collected, the researchers computed a 96 percent confidence interval for the true difference between the proportions of adult females minus the proportion of adult males who use 2 or more credit/debit cards. The confidence interval is: (0.013, 0.049). Assume all checks have been verified.
Question:
Choose the best answer below concerning the confidence interval for the difference between the true proportions of adult females minus the true proportion of adult males who use 2 or more credit/debit cards.

Answers

Answer 1

Using the z-distribution, it is found that the correct option is:

[tex]p_1 - p_2 \pm z\sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]

A confidence interval is given by:

[tex]p \pm zs[/tex]

In which:

p is the estimate of the proportion.z is the critical value.s is the standard error.

In this problem, the proportions are:

A proportion [tex]p_1[/tex] in a sample of size [tex]n_1[/tex].[tex]p_2[/tex] in a sample of size [tex]n_2[/tex].

Hence, the standard errors are:

[tex]s_1 = \sqrt{\frac{p_1(1 - p_1)}{n_1}}, s_2 = \sqrt{\frac{p_2(1 - p_2)}{n_2}}[/tex]

When two proportions are subtracted, the estimate is the subtraction of proportions, while the standard error of the subtraction is the square root of the sum of each standard error squared, hence:

[tex]p = p_1 - p_2[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]

Thus, the interval is:

[tex]p_1 - p_2 \pm z\sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]

A similar problem is given at https://brainly.com/question/12517818

Related Questions

verify cos(a+b)/cos(a) cos(b) =1-tan(a) tan(b)

Answers

The identity as been verified/proved as:

[tex]1 - \tan\ a\ tan\ b = 1 - \tan\ a\ tan\ b[/tex]

Given that:

[tex]\frac{\cos(a + b)}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b[/tex]

Apply cosine identity to the numerator

[tex]\frac{\cos\ a\ cos\ b - \sin a\ sin\ b}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b[/tex]

Split the fraction:

[tex]\frac{\cos\ a\ cos\ b}{\cos\ a\cos b} - \frac{\sin a\ sin\ b}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b[/tex]

Cancel out common terms

[tex]1 - \frac{\sin a\ sin\ b}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b[/tex]

In trigonometry, we have:

[tex]\frac{\sin \theta}{\cos \theta} = \tan \theta[/tex]

So, the equation becomes:

[tex]1 - \tan\ a\ tan\ b = 1 - \tan\ a\ tan\ b[/tex]

Hence, the identity has been verified

Read more about trigonometry identities at:

https://brainly.com/question/21055284

The sample size needed to estimate the difference between two population proportions to within a margin of error E with a significance level of ? can be found as follows. In the expression
E=z?p1(1?p1)n1+p2(1?p2)n2?????????????????????????
we replace both n1 and n2 by n (assuming that both samples have the same size) and replace each of p1, and p2, by 0.5 (because their values are not known). Then we solve for n, and get
n=(z?)22E2.
Finally, increase the value of n to the next larger integer number.
Use the above formula and Table C to find the size of each sample needed to estimate the difference between the proportions of boys and girls under 10 years old who are afraid of spiders. Assume that we want a 99% confidence level and that the error is smaller than 0.07.
n=______.

Answers

Answer:

n= (z)22E2

n=10× 99%÷ 0.07

Does the graph represent a function and if so, why?

A.Yes, no two ordered pairs on this graph have the same second element.
B.Yes, there is more than one ordered pair on this graph.
C.Yes, no two ordered pairs on this graph have the same first element.
D.No, there is a limited number of ordered pairs on this graph.

Answers

Answer:

A. yes

Step-by-step explanation:

Given that f(x) = logo x, write a function that translates f(x) down 4 units and then
reflects it across the x axis.

Answers

Answer:

Answer 2/B

Step-by-step explanation:

The one with Parentheses

-(log6 x-4)

find two ordered pairs for x-4y=2

Answers

Answer:

x-4y=2 can be written as y=(x-2)/4

(2,0) when x=2, y=0 and (6,1) when x=6, y=1

According to an independent research, a point estimate of the proportion of U.S. consumers of black tea is p = 0.76. Calculate the sample size needed to be 95% confident that the error in estimating the true value of p is less than 0.015? Use the z-value rounded to two decimal places to obtain the answer. 4072.69

Answers

Answer:

The sample size needed is 3115.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

Point estimate:

[tex]\pi = 0.76[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Calculate the sample size needed to be 95% confident that the error in estimating the true value of p is less than 0.015?

This is n for which M = 0.015. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.015 = 1.96\sqrt{\frac{0.76*0.24}{n}}[/tex]

[tex]0.015\sqrt{n} = 1.96\sqrt{0.76*0.24}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.76*0.24}}{0.015}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.76*0.24}}{0.015})^2[/tex]

[tex]n = 3114.26[/tex]

Rounding up:

The sample size needed is 3115.

find the amount of time to the nearest day it would take a deposit of $2500 to grow to $1 million at 2% compounded continuously. find how many days & years

Answers

Answer:

Years = natural log (Total / Principal) / Rate

Years = natural log (1,000,000 / 2,500) / .02

Years = natural log (400) / .02

Years = 5.9914645471 / .02

It would take 299.573227355 Years

Source: http://www.1728.org/rate2.htm

Step-by-step explanation:

what should be added to 7777 to get 4999

Answers

We should not add we should subtract -2778

Show all work to identify the asymptotes and zero of the function f(x)=6x/x^2-36

Answers

9514 1404 393

Answer:

asymptotes: x = ±6

zero: x = 0

Step-by-step explanation:

The vertical asymptotes of the function will be at the values of x where the denominator is zero. The denominator is x^2 -36, so has zeros for values of x that satisfy ...

x^2 -36 = 0

x^2 = 36

x = ±√36 = ±6

The vertical asymptotes of the function are x = -6 and x = +6.

The zero of the function is at the value of x that makes the numerator zero. This will be the value of x that satisfies ...

6x = 0

x = 0 . . . . . divide by 6

The zero of the function is x=0.

As a check on this work, we have had a graphing calculator graph the function and identify the zero.

The critical value of F for an upper tail test at a 0.05 significance level when there is a sample size of 21 for the sample with the smaller variance and there is a sample size of 9 for the sample with the larger sample variance is _____. a. 2.94 b. 2.45 c. 2.10 d. 2.37

Answers

Answer:

2.45

Step-by-step explanation:

Given that :

α = 0.05

Larger sample variance= numerator, sample size = 9

Smaller sample variance = denominator, sample size = 21

Hence,

DFnumerator = n - 1 = 9 - 1 = 8

DFdenominator = n - 1 = 21 - 1 = 20

Critical value for upper tail test using the F distribution table at α = 0.05 ; DFnumerator on horizontal ; Df denominator as vertical ;

F critical = 2.447

F critical = 2.45

help with math it would help with summer school

Answers

Answer:

[tex]A). \ \ \frac{(72\pi + 9\pi )}{4} \ in^2[/tex]

Step-by-step explanation:

Given;

radius of the circle, r = 9 inches

the part of the circle cut out = one-forth of the complete circle

the angle of the sector cut out θ= ¹/₄ x 360 = 90⁰

Area of the complete circle = πr² = π x 9² = 81π in²

Area of the sector cut out = [tex]= \frac{\theta }{360} \pi r^2 = \frac{90}{360} \pi (9^2) = \frac{1}{4} \times 81\pi = \frac{81 \pi}{4} = \frac{(72\pi + 9\pi)}{4} \ in^2[/tex]

Therefore, the only correct option is A. [tex]\frac{(72\pi + 9\pi )}{4} \ in^2[/tex]

A data set includes data from student evaluations of courses. The summary statistics are n=89, x=3.44, s=0.67. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 3.50. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
What are the null and alternative hypotheses?
A.
H0: μ=3.50
H1: μ>3.50
B.
H0: μ=3.50
H1: μ<3.50
C.
H0: μ≠3.50
H1: μ=3.50
D.
H0: μ=3.50
H1: μ≠
(I also need the test statistic and p-value) thank you so much in advance :)

Answers

We're told that "the claim that the population of student course evaluations has a mean equal to 3.50". So this means μ=3.50 makes up the null H0

The alternative would be H1: μ ≠ 3.50 since it's the opposite of the claim made in the null.

We go with answer choice D to form the null and alternative hypotheses.

The sign ≠ in the alternative hypothesis tell us that we have a two tail test.

---------------------------------------

Let's compute the test statistic

z = (xbar - mu)/(s/sqrt(n))

z = (3.44 - 3.50)/(0.67/sqrt(89))

z = -0.84483413122896

z = -0.84

The test statistic is roughly -0.84

---------------------------------------

Despite not knowing what sigma is (aka the population standard deviation), we can see that n > 30 is the case. So we can use the Z distribution. This is the standard normal distribution. When n > 30, the T distribution is fairly approximately the same as the Z distribution.

Use a calculator or a Z table to determine that

P(Z < -0.84) = 0.2005

which is approximate

Because we're doing a two-tail test, this means we double that result to get 2*0.2005 = 0.401

The p-value is roughly 0.401

-----------------------------------------

Since the p-value is larger than alpha = 0.05, we don't have enough evidence to reject the null. So you can say that we fail to reject the null, or we accept the null.

The conclusion based on that means that μ=3.50 must be true (unless other evidence comes along to disprove this). In other words, the mean evaluation score from students appears to be 3.50

Identify the terminal point for a 45° angle in a unit circle.
O A (231)
O B.
O c.
V2 72

Answers

Answer:

Step-by-step explanation:

x- coordinate = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]

y- coordinate = sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]

That is ( [tex]\frac{\sqrt{2} }{2}[/tex] , [tex]\frac{\sqrt{2} }{2}[/tex] ) → D

Working at home: According to the U.S Census Bureau, 41% of men who worked at home were college graduates. In a sample of 506 women who worked at home, 166 were college graduates. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 (a) Find a point estimate for the proportion of college graduates among women who work at home. Round the answer to at least three decimal places. The point estimate for the proportion of college graduates among women who work at home is .

Answers

Solution :

a). The point estimate of proportion of college graduates among women who work at home,

[tex]$\hat p =\frac{166}{506}$[/tex]

= 0.3281

99.5% confidence interval

[tex]$=\left( \hat p \pm Z_{0.005/2} \sqrt{\frac{\hat p (1- \hat p)}{n}} \right)$[/tex]

[tex]$=\left( 0.3281 \pm 2.81 \sqrt{\frac{0.3281 \times (1- 0.3281)}{506}} \right)$[/tex]

[tex]$=(0.3281 \pm 0.0586)$[/tex]

[tex]$=(0.2695, 0.3867)$[/tex]

Which is equivalent to 10’6

Answers

Answer:

35/5 (if you mean 10.6)

1000000 (if you mean 10 to the sixth power)

0.000001 (if you mean 10/6)

Probably 0.5 if angle t is measured from the positive x axis.

evaluate
(3^-1+4^-1)^-2

Answers

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{= (3^{-1}+4^{-1})^{-2}}\\\\\\\mathsf{3^{-1} = \bf {\dfrac{1}{3}}}\\\\\\\mathsf{4^{-1} = \bf \dfrac{1}{4}}\\\\\\\mathsf{= (\dfrac{1}{3}+\dfrac{1}{4})^{-2}}\\\\\\\mathsf{\dfrac{1}{3} + \dfrac{1}{4} = \bf \dfrac{7}{12}}\\\\\\\mathsf{= (\dfrac{7}{12})^{-2}}\\\\\large\text{Simplify above and you have your overall answer...}\\\\\\\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf \dfrac{144}{49}}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}\\\\\\\\\frak{Amphitrite1040:)}[/tex]

Team A scored 30 points less than four times the number of points that Team B scored. Team C scored 61 points more than half of the number of points that Team B scored. If Team A and Team C shared in the victory, having earned the same number of points, how many more points did each team have than Team B?

Answers

Answer:

team a and team c scored 74 points which is 48 points more than team b, scoring 26 points.

Step-by-step explanation:

Pam’s eye-level height is 324 ft above sea level, and Adam’s eye-level height is 400 ft above sea level. How much farther can Adam see to the horizon? Use the formula d = StartRoot StartFraction 3 h Over 2 EndFraction EndRoot, with d being the distance they can see in miles and h being their eye-level height in feet.
1 mi
StartRoot 6 EndRoot mi
19 mi
19 StartRoot 6 EndRoot mi

Answers

9514 1404 393

Answer:

(b) √6 mi

Step-by-step explanation:

Putting the given heights into the formula, we find the difference in distances to be ...

Adam' horizon distance = √((3/2)(400)) = 10√6 . . . miles

Pam's horizon distance = √((3/2)(324)) = 9√6 . . . . miles

Then the difference Adam can see is farther than the distance Pam can see by ...

10√6 -9√6 = √6 . . . miles

Write a quadratic equation in standard form that has two solutions, 9 and -2

(the leading coefficient must be 1.)

Answers

(x - 9)(x + 2) = 0
x^2 + 2x -9x -18 = 0
x^2 - 7x - 18 = 0

In a survey of 938 U.S. adults, 235 say the phrase "you know" is the most annoying conversational phrase. Let p be the proportion of the population who respond yes. Use the given information to Construct a 90% confidence interval for p.

Answers

Answer:

CI 90% = ( 0.227 ; 0.273)

Step-by-step explanation:

Information from the survey:

sample size n = 938

number of people with yes answer x = 235

proportion of people p = 235/938

p = 0.25 then q = 1 - 0.25 q = 0.75

Confidence Interval 90 % .

CI 90% = ( p ± SE )

CI 90% = ( p ± z(c)*√(p*q)/n)

CI 90 % then significance level is α = 10 % α/2 = 5%

α/2 = 0.05 we find in z-table z (c) = 1.64

√(p*q)/n = √0.25*0.75/938

√(p*q)/n = √0.000199

√(p*q)/n = 0.014

CI 90% = ( p ± z(c)*√(p*q)/n)

CI 90% = ( 0.25 ± 1.64*0.014)

CI 90% = ( 0.25 ± 0.023 )

CI 90% = ( 0.227 ; 0.273)

how to work this fraction 4/11+5/22+3/44

Answers

Answer:

29/44

Step-by-step explanation:

[tex]\frac{4}{11} +\frac{5}{22} +\frac{3}{44} =\\[/tex]

-find the common denominator

[tex]\frac{4*4}{4*11} + \frac{2*5}{2*22} +\frac{3}{44} =[/tex]

[tex]\frac{16}{44} +\frac{10}{44} +\frac{3}{44} =[/tex]

-add the fractions and solve

[tex]\frac{16+10+3}{44} =[/tex]

[tex]\frac{29}{44}[/tex]

Which of the following statements correctly explains the meaning of the term "95% confidence" in the confidence statement? The interval 52% to 58% is based on a procedure that includes a sample representing 95% of population. The interval 52% to 58% is based on a procedure that includes the true population value 95% of the time. The interval 52% to 58% is based on a procedure that produces a margin of error (of ±3) 95% of the time.

Answers

Answer:

The interval 52% to 58% is based on a procedure that includes the true population value 95% of the time.

Step-by-step explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

95% confidence

We are 95% sure that the interval contains the true mean/proportion, and thus, the correct option is:

The interval 52% to 58% is based on a procedure that includes the true population value 95% of the time.

Find the cash value of the lottery jackpot (to the nearest dollar). Yearly jackpot payments begin immediately (26 for Mega Millions and 30 for Powerball). Assume the lottery can invest at the given interest rate. Powerball: $360 million; 5.4% interest
a. $188,347,953
b. $282,573,702
c. $185,870,742
d. $298,386,685

Answers

Answer:

The right response is Option c ($185,870,742).

Step-by-step explanation:

Given:

n = 30

r = 5.4%

or,

= 0.054

Periodic payment will be:

[tex]R = \frac{360000000}{30}[/tex]

[tex]=12000000[/tex] ($)

Now,

The present value will be:

= [tex]R+R(\frac{1-(1+r)^{-n+1}}{r} )[/tex]

By substituting the values, we get

= [tex]12000000+12000000(\frac{1-(1+0.054)^{-30 + 1}}{0.054} )[/tex]

= [tex]12000000+12000000\times 14.4892[/tex]

= [tex]185,870,742[/tex] ($)

what is 127/14 simplified?

Answers

It’s would be 9 1/4

Answer:

9 1/14

Step-by-step explanation:

127 ÷14

127 divided by 14 equals

9 with a remainder of 1

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