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
Radda [10]
3 years ago
12

A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is chang

ing over time. A recent sample of 1,000 adults showed 410 indicating that their financial security was more than fair. Suppose that just a year before, a sample of 1,200 adults showed 420 indicating that their financial security was more than fair.
Required:
a. State the hypotheses that can be used to test for a significant difference between the population proportions for the two years.
b. Conduct the hypothesis test and compute the p-value. At a 0.05 level of significance, what is your conclusion?
c. What is the 95% confidence interval estimate of the difference between the two population proportions?
d. What is your conclusion?
Mathematics
1 answer:
IgorLugansk [536]3 years ago
5 0

Answer:

b) Then z(s) is in the rejection region for H₀. We reject H₀. The p-value is smaller than α/2

c)CI 95 %  =  ( 0.00002 ;  0.09998)

Step-by-step explanation: In both cases, the size of the samples are big enough to make use of the approximation of normality of the difference of the proportions.

Recent Sample

Sample size    n₁  =  1000

Number of events of people with financial fitness more than fair

x₁  =  410

p₁ =  410/ 1000  =  0.4     then q₁ = 1 - p₁    q₁ =  1 -  0.4    q₁  = 0.6

Sample a year ago

Sample size    n₂ =  1200

Number of events of people with financial fitness more than fair

x₂  =  420

p₂  =  420/1200     p₂ = 0.35   q₂  =  1 - p₂    q₂  = 1 - 0.35   q₂ = 0.65

Test Hypothesis

Null Hypothesis                                  H₀              p₁  =  p₂

Alternative Hypothesis                      Hₐ              p₁  ≠  p₂

CI  95 % then significance level  α  =  5%   α  = 0.05    α/2  = 0.025

To calculate p-value:

SE  =  √ (p₁*q₁)/n₁  +  (p₂*q₂)/n₂

SE  =  √ 0.4*0.6/1000 +  0.65*0.35/1200

SE  =  √ 0.00024 + 0.000189

SE = 0.021

z(s) =  ( p₁ - p₂ ) / SE

z(s) = ( 0.4 - 0.35 )/0.021

z(s) = 0.05/ 0.021

z(s) =  2.38

We find p-value from z-table to be   p-value = 0.00842

Comparing

p-value with  α/2   = 0.025

α/2 >  p-value  

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

CI 95 %  =  ( p₁  -  p₂ )  ±  2.38*SE

CI 95 %  =  ( 0.05 ± 2.38*0.021 )

CI 95 %  =  ( 0.05 ± 0.04998)

CI 95 %  =  ( 0.00002 ;  0.09998)

CI 95 % does not contain the 0 value affirming what the hypothesis Test already demonstrate

You might be interested in
I need to know how to solve this
dedylja [7]

Answer:

C

Step-by-step explanation:

I think you have to call a = 14/32 and b = 7/4

3a = 3 * 14/32 = 42/32

b = 1 3/4 = (4 + 3)/4 = 7/4

42/32 // 7/4                        Invert and multiply

42/32 * 4/7                         Cancel 4 into 32 and 7 into 42

6/8 = 3/4

I make the answer C

3 0
3 years ago
Read 2 more answers
Which set of ordered pairs represents a function?
Paladinen [302]
3 because the numbers for x are all different
5 0
3 years ago
Serafina is solving a number puzzle that involves three integers. Integers, e, f, and g, where e is negative. The product of e a
Alex73 [517]

Answer:

a

Step-by-step explanation:

3 0
3 years ago
When the distributive property is applied, which number completes the statement correctly?
maxonik [38]
-7, because you distribute it to both -4 and 3.2, which means you're multiplying it to both.
7 0
3 years ago
What’s 7^2+15\7^2 ?
Elis [28]
Decimal: )49.306122)
4 0
3 years ago
Other questions:
  • Find the mean of this set of numbers: 19, 19, 9, 11, 13, 20, 19, 10​
    5·1 answer
  • Write the standard form of a line that passes through the given points (4,7) and (0,7)
    12·1 answer
  • A density curve for all the possible ages between 0 years and 100 years is in the shape of a triangle. What is the height of the
    9·2 answers
  • If f(x) = 4x - 20, what is f(4)?<br> O A. -4<br> оо<br> O B. -12<br> O c. 4<br> O D. 16
    13·2 answers
  • Point P was rotated about the origin (0,0) by 105
    10·1 answer
  • —2a — 5 &gt; 3 on a graph
    12·1 answer
  • 70%of $10=$<br> Comlelete the folling statements
    15·1 answer
  • How do you add integers with different signs?
    9·1 answer
  • PLEASE HURRY: Which equation describes the same line as y-5=-2(x+4)
    8·1 answer
  • Ms. Jerome wants to buy identical boxes of art supplies for her 25
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!