mong 500 marriage license applications chosen at random in a givenyear, there were 48 in which the woman was at least one year older than the man, and among400 marriage license applications chosen at random six years later, there were 68 in which thewoman was at least one year older than the man. Construct a 99% confidence interval for thedifference between the corresponding true proportions of marriage license applications in whichthe woman was at least one year older than the man. Interpret the CI in the context of theproblem.

Answer:

CI 99% = (  0,022  ;  0,126 )

Step-by-step explanation:

First sample  

n₁  = 500

x₁  = 48

p₁ = x₁ / n₁   =  48 / 500      p₁  =  0,096      p₁  = 9,6 %

Second sample

n₂  = 400

x₂  = 68

p₂ = x₂ / n₂   =  68 / 400      p₂  =  0,17       p₂  = 17 %

CI = 99 %    significance level α = 1 %     α  = 0,01

z(c)  for α = 0,01  is from z- table    z(c) = 2,325

CI  =  ( p₂ - p₁ ) ±  z(c) *√ p*q* ( 1/n₁  +  1 / n₂ )

Where

p₂  -  p₁  =  0,17 - 0,096 = 0,074

p = ( x₁ + x₂ )  / n₁ + n₂

p =  ( 48  +  68  ) /( 500 + 400)

p = 116/ 900     p = 0,1288     and   q = 1 - p     q  = 0,8712

z(c) *√ p*q* ( 1/n₁  +  1 / n₂ ) = 2,325 * √ 0,1288*0,8712 ( 1 / 500 + 1/ 400)

2,235 * 0,02247

z(c) *√ p*q* ( 1/n₁  +  1 / n₂ ) = 0,052

Then

CI 99 %  =  0,074  ±  0,052

CI 99% = (  0,022  ;  0,126 )

The difference between the groups shows that the proportion in the second group was bigger than in the first group.

The CI in the context of the problem is  CI 99% = (  0,022  ;  0,126 )

Given first sample is  

n₁  = 500

x₁  = 48

  [tex]P_{1} =\dfrac{X_{1} }{n_{1} }[/tex]      [tex]P_{1} =\dfrac{48}{500}[/tex]      

p₁  =  0,096      p₁  = 9,6 %

Given second sample

n₂  = 400

x₂  = 68

[tex]P_{2} =\dfrac{X_{2} }{n_{2} }[/tex]      [tex]P_{2} =\dfrac{68}{400}[/tex]        

p₂  =  0,17       p₂  = 17 %

Since given CI = 99 %    so significance level  α = 1 %     α  = 0,01

From Z-Table  z(c)  for α= 0,01  is = 2,325

CI  =   [tex](P_{2} -P_{1}[/tex]   ±    [tex]Z(c)\sqrt[2]{p\times q} (\dfrac{1}{n_{1} } +\dfrac{1}{n_{2} } )[/tex]  

Where

p₂  -  p₁  =  0,17 - 0,096 = 0,074

[tex]P= \dfrac{X_{1} +X_{2} }{n_{1}+n_{2} }[/tex]

[tex]P=\dfrac{48+68}{500+400}[/tex]

[tex]P=\dfrac{116}{900}[/tex]

p = 0,1288     and   q = 1 - p     q  = 0,8712

[tex]Z(c)\sqrt[2]{p\times q} (\dfrac{1}{n_{1} } +\dfrac{1}{n_{2} } )[/tex]  [tex]2325\times\sqrt[2]{0.1288\times 0.8712} (\dfrac{1}{500_{} } +\dfrac{1}{400_{} } )[/tex]

  [tex]Z(c)\sqrt[2]{p\times q} (\dfrac{1}{n_{1} } +\dfrac{1}{n_{2} } )=0.052[/tex]

Then

CI 99 %  =  0,074  ±  0,052

CI 99% = (  0,022  ;  0,126 )

Hence the difference between the groups shows that the proportion in the second group was bigger than in the first group.

To know more about Chi square follow

https://brainly.com/question/4543358

Can someone please help

a student needs to fill a 12 gallon fish tank. The student has a container that holds 1/3 gallon of water. how many times will the student need to fill the container with water in order to fill the fish tank completely

And 50% what is the answer please help no links no links

What is the difference/ ratio of the numbers 6.25, 25, 100, 400,

During second period, Mia completed a grammar worksheet. Of the 60 questions, Mia got 80% right. How many questions did Mia get right?

What is the radius of a hemisphere with a volume of 757 cm", to the nearest tenth of
a centimeter?

Ken flips a coin and draws a card. Is this a independent or dependent event?

Solve for x and y:
Ty– 5x = 45
x = 8 - 2y
O x = 5, y = 10
O x = 5, y = -2
x = -2, y = 5
O x = 4, y = 2

factor by grouping 20i^3-25i^2+4i-5

50 points) please help! no links, brainliest, extra points.

I understand if you need points, you can go to my old questions and answer them for points, please only answer if your 100% sure you're correct. I've redone this over 20 times, asked over 50, and failed all those times. thank uu.


Any non-integer answers in this problem should be entered as decimals rounded to the tenth.

Duncan surveyed 10 people to see how many hours per week they exercise. The results are listed below.


18, 13, 20, 14, 12, 6, 11, 5, 15, 10


Use the data set to complete the sentences.


The interquartile range of the data set is _____.


The mean absolute deviation of the data set is _____.

Mr. Bryant earns $32 per hour. He regularly works 40 hours per week. If he works 26 overtime hours (at time- and-a-half), would his overtime pay exceed his regular gross pay? Explain your answer.​

I'll try to give Brainlyest please help!!

520 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 4 hours. How long would it be, to the nearest tenth of an hour, until there are 33980 bacteria present?

Tracy is trying to justify a step in her paragraph proof. What is the property that she should use?
ABAB
1)Transitive Property of
Congruence
2)Symmetric Property of
Congruence
3)Reflexive Property of Congruence
4)Equality of Congruence Property

The sum of −7 times a number and 8 times the sum of the number and 1 is the same as the number minus 7.

PLEASE HELP !! ILL GIVE BRAINLIEST !!

PLEASE HELP !! ILL GIVE BRAINLIEST !! Ohh

Using an applet, we found that the theory-based test results in a t-statistic of -7.25 and p-value less than 0.0001. State your conclusion in the context of the study.

a. We have very strong evidence that the long-run average guess of the population size of Milwaukee, Wisconsin is smaller with the anchor of Chicago than with the anchor of Green Bay.
b. We have very strong evidence that the long-run average guess of the population size of Milwaukee, Wisconsin is smaller with the anchor of Green Bay than with the anchor of Chicago.
c. We have very weak evidence that the long-run average guess of the population size of Milwaukee, Wisconsin is larger with the anchor of Green Bay than with the anchor of Chicago.
d. We have very weak evidence that the long-run average guess of the population size of Milwaukee, Wisconsin is larger with the anchor of Chicago than with the anchor of Green Bay.

please help me i will mark brainliest! :D

Which of the following can be determined exactly from a histogram? A. mean B. median O C. MAD D. none of these​

James wanted to fence in his backyard for his dog Remi. The yard has a length of 12 feet and a width of 4 feet. What is the area and perimeter of the fenced yard?



A= P =

7. Logan can type 45 words in 2 minutes. Ebony can type 22 words in 45 seconds. Who
types slower?

The function f is defined by f(x) = 5x2 + 2x + 5. What is the value of f(2)?

The following 5 questions are based on this information: An economist claims that average weekly food expenditure of households in City 1 is more than that of households in City 2. She surveys 35 households in City 1 and obtains an average weekly food expenditure of $164. A sample of 30 households in City 2 yields an average weekly expenditure of $159. Historical data reveals that the population standard deviation for City 1 and City 2 are $12.50 and $9.25, respectively.

Required:
At the 5% significance level, is the economist claim supported by the data?

write 10075302 in words in both the Indian system and international system and rearrange the digits to get the smallest number ​

what is 20 x 3-4 + 80 / 988 + 444444 x 343

Which expressions are equivalent to the given expression?v252

CAN SOMEONE PLEASE ANSWER THIS FOR ME

hi!
which equation is graphed here?

BRAINLIESTT!!
13POINTS
A construction crew built 1/2 miles of road in 1/4 days.
What is the unit rate in miles per day?

Write your answer in simplest form.