answer.
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]
2 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]2 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 water trough has two congruent isosceles trapezoids as ends and two congruent rectangles as sides.
BlackZzzverrR [31]

Answer:

Part a) The exterior surface area is equal to 160\ ft^{2}

Part b) The volume is equal to 240\ ft^{3}

Part c) The volume water left in the trough will be 84\ ft^{3}

Step-by-step explanation:

Part a) we know that

The exterior surface area is equal to the area of both trapezoids plus the area of both rectangles

so

<em>Find the area of two rectangles</em>

A=2[12*5]=120\ ft^{2}

<em>Find the area of two trapezoids</em>

A=2[\frac{1}{2}(8+2)h]

Applying Pythagoras theorem calculate the height h

h^{2}=5^{2}-3^{2}

h^{2}=16

h=4\ ft

substitute the value of h to find the area

A=2[\frac{1}{2}(8+2)(4)]=40\ ft^{2}

The exterior surface area is equal to

120\ ft^{2}+40\ ft^{2}=160\ ft^{2}

Part b) Find the volume

We know that

The volume is equal to

V=BL

where

B is the area of the trapezoidal face

L is the length of the trough

we have

B=20\ ft^{2}

L=12\ ft

substitute

V=20(12)=240\ ft^{3}

Part c)

<em>step 1</em>

Calculate the area of the trapezoid for h=2 ft (the half)

the length of the midsegment of the trapezoid is (8+2)/2=5 ft

A=\frac{1}{2}(5+2)(2)=7\ ft^{2}

<em>step 2</em>

Find the volume

The volume is equal to

V=BL

where

B is the area of the trapezoidal face

L is the length of the trough

we have

B=7\ ft^{2}

L=12\ ft

substitute

V=7(12)=84\ ft^{3}

4 0
2 years ago
The Hoffman family has bought one pizza on Friday night every week for the last 10 years.
wel

Answer:520

Step-by-step explanation:.

8 0
2 years ago
Kendra charges $11 to shovel a driveway. She shoveled 4 driveways on Saturday and then some more on Sunday. She made $143 for th
White raven [17]

Let number of driveways , she shoveled on Sunday = x

And for 4 driveways , Kendra charges = 4*11=44

Therefore,

143 = 44 + 11x

And that's the model for the given situation .

Subtracting 44 from both sides,

143-44 = 11x

99 = 11x

Dividing both sides by 11

x = 9

Therefore she shoveled 9 driveways on Sunday .

7 0
2 years ago
Read 2 more answers
What is the error due to using linear interpolation to estimate the value of sinxsin⁡x at x = \pi/3? your answer should have at
Serhud [2]
<h3>Answer:</h3>
  • using y = x, the error is about 0.1812
  • using y = (x -π/4 +1)/√2, the error is about 0.02620
<h3>Step-by-step explanation:</h3>

The actual value of sin(π/3) is (√3)/2 ≈ 0.86602540.

If the sine function is approximated by y=x (no error at x = 0), then the error at x=π/3 is ...

... x -sin(x) @ x=π/3

... π/3 -(√3)/2 ≈ 0.18117215 ≈ 0.1812

You know right away this is a bad approximation, because the approximate value is π/3 ≈ 1.04719755, a value greater than 1. The range of the sine function is [-1, 1] so there will be no values greater than 1.

___

If the sine function is approximated by y=(x+1-π/4)/√2 (no error at x=π/4), then the error at x=π/3 is ...

... (x+1-π/4)/√2 -sin(x) @ x=π/3

... (π/12 +1)/√2 -(√3)/2 ≈ 0.026201500 ≈ 0.02620

6 0
2 years ago
Jeanne wants to start collecting coins and orders a coin collection starter kit. The kit comes with three coins chosen at random
lesya692 [45]
Conditional probability is a measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B), or sometimes P_B(A).

The conditional probability of event A happening, given that event B has happened, written as P(A|B) is given by
P(A|B)= \frac{P(A \cap B)}{P(B)}

In the question, we were told that there are three randomly selected coins which can be a nickel, a dime or a quarter.

The probability of selecting one coin is \frac{1}{3}

Part A:
To find <span>the probability that all three coins are quarters if the first two envelopes Jeanne opens each contain a quarter, let the event that all three coins are quarters be A and the event that the first two envelopes Jeanne opens each contain a quarter be B.

P(A) means that the first envelope contains a quarter AND the second envelope contains a quarter AND the third envelope contains a quarter.

Thus P(A)= \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1}{27}

</span><span>P(B) means that the first envelope contains a quarter AND the second envelope contains a quarter

</span><span>Thus P(B)= \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}

Therefore, P(A|B)=\left( \frac{ \frac{1}{27} }{ \frac{1}{9} } \right)= \frac{1}{3}


Part B:
</span>To find the probability that all three coins are different if the first envelope Jeanne opens contains a dime<span>, let the event that all three coins are different be C and the event that the first envelope Jeanne opens contains a dime be D.
</span><span>
P(C)= \frac{3}{3} \times \frac{2}{3} \times \frac{1}{3} = \frac{6}{27} = \frac{2}{9}

</span><span>P(D)= \frac{1}{3}</span><span>

Therefore, P(C|D)=\left( \frac{ \frac{2}{9} }{ \frac{1}{3} } \right)= \frac{2}{3}</span>
3 0
2 years ago
Other questions:
  • Stock in trochel office supplies trades at $72.40 per share and pays a yearly dividend of $6.92 per share. if david owns stock i
    13·2 answers
  • The volume of water in a resevoir decreases 21,000 cubic yards over a 3-month period. What is the average change in volume per m
    7·2 answers
  • What is the ratio of 16 cm and 448m
    9·2 answers
  • Felipe is planning a party. He has $50.00 to spend on sandwiches that cost $2.50 per person, $25.00 to spend on drinks that cost
    11·2 answers
  • You have just spoken to your insurance agent and you are interested in investing in a 20-Payment Life insurance policy. Given th
    7·2 answers
  • For a polygon to be convex means that all of its interior angles are less than 180 degrees. Prove that for all integers n ≥ 3, t
    5·1 answer
  • Throughout the 2016 Presidential election primaries, Millennials (those aged 20 t 36 years) consistently supported Senator Berni
    8·1 answer
  • PLEASE HELP WILL GIVE BRAINLIEST
    13·1 answer
  • Given line m is parallel to line n. What theorem or postulate justifies the statement? ∠1 ≅ ∠4 Corresponding angles postulate Al
    12·1 answer
  • How much water and how much drink mix should Jerome use to make enough energy drink for all the runners? Create a table to show
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!