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
joja [24]
3 years ago
13

Exercise 6.22 provides data on sleep deprivation rates of Californians and Oregonians. The proportion of California residents wh

o reported insufficient rest or sleep during each of the preceding 30 days is 8.0%, while this proportion is 8.8% for Oregon residents. These data are based on simple random samples of 11,545 California and 4,691 Oregon residents. (a) Conduct a hypothesis test to determine if these data provide strong evidence the rate of sleep deprivation is different for the two states. (Reminder: Check conditions) (b) It is possible the conclusion of the test in part (a) is incorrect. If this is the case, what type of error was made?
Mathematics
1 answer:
kherson [118]3 years ago
5 0

Answer:

a. The alternative hypothesis H₀: p'₁ ≠ p'₂ is accepted

b. Type I error

Step-by-step explanation:

Proportion of California residents who reported insufficient rest = 8.0%

Proportion of Oregon  residents who reported insufficient rest = 8.8%

p'₁ = 0.08 * 11545 =923.6

p'₂ = 0.088 * 4691=412.81

σ₁ = \sqrt{n*p_1*q_1}  = \sqrt{n*p_1*(1-p_1)} = \sqrt{11545*0.08*(1-0.08)} = 29.15

σ₂ = \sqrt{n*p_2*q_2}  = \sqrt{n*p_2*(1-p_2)}= \sqrt{4691*0.088*(1-0.088)} = 19.40

Samples size of California residents n₁ = 11,545

Samples size of Oregon residents n₂ = 4,691

Hypothesis can be constructed thus

Let our null hypothesis be H ₀: p'₁ = p'₂

and alternative hypothesis H ₐ: p'₁ ≠ p'₂

Then we have  

z =\frac{(p'_1 -p'_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2} } }

The test statistics can be computed by

     

t₀ = \sqrt{\frac{n_1n_2(n_1+n_2-2)}{n_1+n_2} } *\frac{p_1'-p_2'}{\sqrt{(n_1-1)\sigma_1^2+(n_2-1)\sigma_2^2} } =      1104.83

c from tables is   P(T ≤ c) = 1 - α where α = 5% and c = 1.65

since t₀ ≥ c then then the hypothesis is rejected which means the alternative hypothesis is rejected

b. Type I error, rejecting a true hypothesis

You might be interested in
A cylinder has a radius of 4x + 2 and a height of 5x + 4. Which polynomial in standard form best describes the total volume of t
Olenka [21]
Area of the base = pi*(4x+2)^2 = pi*(16x^2 +16x +4)

volume of cylinder = pi*r^2 *h 

V = pi *(16x^2 +16x +4)(5x+4) = pi*(80x^3 +80x^2 +20x +64x^2 +64x +16) = 

= pi*(80x^3 +144x^2 +84x +16)

than we consider it without pi so result choice A. is right sure 

hope helped 
3 0
2 years ago
Read 2 more answers
Please help 0.8t+0.6t-t
PolarNik [594]

Answer:

0.4t

Step-by-step explanation:

1.4t-t=0.4t

Hope this helps :)

3 0
3 years ago
Read 2 more answers
In AGHI, the measure of ZI=90°, HI = 5.6 feet, and IG = 2.8 feet. Find the measure
lesantik [10]

Answer:

63.4

Step-by-step explanation:

4 0
3 years ago
Q4.
xenn [34]

Answer:

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Please help if you can :)
VikaD [51]

the domain of the function graphed above of

F,IF,B,5

Answer: 909.0

7 0
3 years ago
Other questions:
  • Which expression is tge simplest form of -(4x+y)+2(x-3y)​
    9·2 answers
  • (2 thousands 7 tens) ÷ 10 =
    14·2 answers
  • What is 2 times 2 divided by 55
    15·1 answer
  • 16/3 simplify the answer using a mixed number or a whole number
    8·2 answers
  • MY PASSWORD AND USERNAME IS 592799999.592799999
    12·1 answer
  • Simplify the following fraction: 10/24
    10·2 answers
  • Someone please help me I know you see this:)
    10·2 answers
  • The company wants to use the package that has the
    6·1 answer
  • HELP PLEASE !! <br> IS IT A, B OR C
    10·1 answer
  • GIVING BRAINLEST TO THE PERSON THAT CAN EXPLAIN HOW TO DO THIS THE BEST :)
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!