1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
igor_vitrenko [27]
2 years ago
8

A company surveyed adult Americans about their consumer debt. They reported that 48% of Millennials (those born between 1980 and

1996) and 60% of Gen Xers (those born between 1965 and 1971) did not pay off their credit cards each month and therefore carried a balance from month to month. Suppose that these percentages were based on representative samples of 450 Millennials and 300 Gen Xers. Is there convincing evidence that the proportion of Gen Xers who do not pay off their credit cards each month is greater than this proportion for Millennials
Mathematics
1 answer:
sergeinik [125]2 years ago
6 0

Answer:

We reject H₀ at 95 % of CI the group of Gen Xers who do not pay their credit card each month, is greater than this proportion for Millennians

Step-by-step explanation:

Sample proportion 1: Born between 1980 and 1996

sample size    n₁  = 450

p₁  =  0,48        p₁ = 48 %

x₁ = 0,48 * 450        x₁ = 216

Sample proportion 2:  Born between 1965 and 1971

sample size    n₂  = 300

p₂ =  0,60         p₂ = 60%

x₂  = 0,6* 300     x₂  = 180

Test Hypothesis:

Null Hypothesis                          H₀               p₂  =   p₁

Alternative Hypothesis              H                p₂  >  p₁

Samples both big enough to use the normal distribution as an approximation to the binomial distribution.

We assume  CI = 95 %   then significance level α   = 5 %  the alternative hypothesis tells us that we need to develop a one-tail test to the right.

z-score  is z(c)  for  α = 0,05       from z-table   z(c) = 1,64

To calculate z(s)

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

p₂ - p₁  =  0,60  - 0,48

p₂ - p₁  =  0,12

p = ( x₁ + x₂ ) / n₁ + n₂

p = ( 216  + 300) / 450 + 300

p = 516 / 750     p = 0,688      then   q = 1 - p     q = 0,312

z(s) = 0,12 / √ 0,688*0,312* ( 1/450) + 1/ 300)

z(s) = 0,12 / √ 0,2146* ( 0,0022 + 0,0033)

z(s) = 0,12 / √ 0,001192

z(s) = 0,12/ 0,03452

z(s) = 3,47

Comparing |z(c)|   and |z(s)|

z(s) > z(c)

Then z(s) is in the rejection region. We reject H₀.

We can support the  claim that the proportion of the group Gen Xers who do not pay their credit card is greater than Millennians

You might be interested in
What's the LCF of 12, 27, and 36?
Fudgin [204]
3.....................
7 0
3 years ago
Read 2 more answers
The square root of 68 is between what two consecutive whole numbers
Pavel [41]
The two consecutive numbers are 8 and 9.
4 0
3 years ago
What is the answer please?
docker41 [41]

Answer: D (bottom option)

Not Congruent

Step-by-step explanation:

Assuming the trapezoids are to scale, they are not the same shape. This means that they could not be congruent even if they were centered on top of each other.

3 0
1 year ago
I know the answer but I need help doing the equation!!! 10 points!!!! Help!!!!
Brums [2.3K]

Answer: Here x = 9. This is the correct answer. Hooe it helps

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Would 64, 32, and 24 inch perimeter make a triangle?
Harlamova29_29 [7]

Answer:

no

Step-by-step explanation:

the two smaller numbers added together need to be greater than or equal to the larger number

8 0
3 years ago
Other questions:
  • What's the pattern for 1,3,5,7,5,3,1,3
    5·1 answer
  • If f ( 4 ) = − 2 , write an ordered pair that must be on the graph of y = f ( x + 4 ) + 1
    6·1 answer
  • 16/7 - 1/14 subtracting fractions
    6·1 answer
  • PLEASE HELP TIMED!
    5·2 answers
  • ^DEF and ^RSQ are shown in the diagram below
    13·1 answer
  • Cindy bought 3 burgers and 2 soft drinks for $10.50. At the same restaurant, Sean bought 4 burgers and 3 soft drinks for 14.50.
    5·1 answer
  • K & Christian each have a garden of the same size and shape cake grows flowers one and six her of her garden Christian grows
    5·1 answer
  • Given that the line PQ has P(4, 1) and gradient ½, determine the equation of this line.​
    11·1 answer
  • 10 Rotate the point (7, 8) around the origin 90 degrees. State the image of the
    11·2 answers
  • निम्नलिखित वाक्यों को पढ़िए और रिक्त स्थानों में उचित निपात शब्द भरिए-
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!