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
UNO [17]
3 years ago
12

Sleep deprivation, CA vs. OR, Part I. According to a report on sleep deprivation by the Centers for Disease Control and Preventi

on, the proportion of California residents who 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. Calculate a 95% confidence interval for the difference between the proportions of Californians and Oregonians who are sleep deprived and interpret it in context of the data.
Mathematics
1 answer:
vlabodo [156]3 years ago
7 0

Answer:

0.008±0.0095=(-0.0015,0.0175)

Step-by-step explanation:

In this case we must use the formula to calculate the confidence interval for the difference between two proportions given by inferential statistics. The formula to calculate both limits of the interval is as it follows:

(p_{1}-p_{2} )+\sqrt[]{\frac{p_{1}(1-p_{1})}{n_{1} }+\frac{p_{2}(1-p_{2})}{n_{2}}  } \\(p_{1}-p_{2} )-\sqrt[]{\frac{p_{1}(1-p_{1})}{n_{1} }+\frac{p_{2}(1-p_{2})}{n_{2}}  }

Where:

p_{1}: proportion of population one (in our case: Oregon residents who reported insufficient rest or sleep)

p_{2}: proportion of population two (in our case: California residents who reported insufficient rest or sleep)

z_{(∝/2)}: quantile of the normal distribution with α/2 probability (in our case, from the standard normal table we have 1.96 for a confidence level of 95%)

n_{1}: sample size for population one (in our case, sample of Oregon residents)

n_{2}: sample size for population two (in our case, sample of California residents)

Now, with our data we have:

p_{1}=0.088  

p_{2}=0.08  

z_{(∝/2)}=1.96  

n_{1}=4,691  

n_{2}=11,545  

Therefore, we obtain:

(0.088-0.08)+1.96\sqrt{\frac{0.088(1-0.088)}{4,691}+\frac{0.08(1-0.08)}{11,545} } \\(0.088-0.08)-1.96\sqrt{\frac{0.088(1-0.088)}{4,691}+\frac{0.08(1-0.08)}{11,545} }

Finally, the result for our interval:

0.008+0.0095=(-0.0015,0.0175)

According to the result we can say with a 95% confidence, that the proportion of Oregon residents with sleep deprivation issues is the same as the proportion of California residents. The reason for this is that 0 (zero) is contained within the interval.

You might be interested in
Write an equivalent unit rate of eating 4 hot dogs in 1/3 of a minute
zysi [14]

Answer:8

Step-by-step explanation:

I'm smort

3 0
2 years ago
Read 2 more answers
A park is 4 times as it is wide. If the distance around the park is 12.5 kilometers what is the area of the park
MaRussiya [10]

Answer:

6.25 km

Step-by-step explanation:

Here is the correct question: A park is 4 times as long as it is wide. If the distance around the park is 12.5 kilometers, what is the area of the park?

Given: Perimeter (Distance) of the park= 12.5 km

Considering park is in rectangular shape.  

Let the width of park be x

∴ as given length will be 4x.

Formula for perimeter of rectangle =2\times (length + width)

Perimeter is given 12.5 km

⇒ 12.5= 2\times (4x+x)

⇒ 12.5= 10x

∴ x= 1.25 km, which means width is 1.25 km and length is 5 km.

Now, finding the area of park

Formula; Area of rectangle= length\times width

∴ Area of rectangle= 5\times 1.25 = 6.25 km

∴Area of park will be 6.25 km.

6 0
3 years ago
Dale tried to estimate the area of his backyard garden. He guessed it was 12 square meters. When he measured the dimensions late
Elena-2011 [213]

Answer:

cool

Step-by-step explanation:

5 0
2 years ago
A map has the scale 1/3inch = 8 miles. If city a and city b are 12 inches apart on my map then how far apart are the city’s in r
Feliz [49]
The equation would be
12 ÷ 1/3 =
12 x 3/1 =
12 x 3 =

36 miles
6 0
2 years ago
Harold bought 2 pairs of sandals for the same price. He also bought a pair of socks for $3. How much did one pair of sandals cos
DochEvi [55]
The answer would be each pair of sandals costed $14
$14+$14=28+$3=$31
6 0
3 years ago
Other questions:
  • miranda says 30×26 is greater than 20×36.is she correct?draw a model to explain if miranda is correct.
    7·1 answer
  • This question shows the power of conserved quantities. consider a particle in a smooth monotonic attractive central potential v
    9·1 answer
  • Does 13, 84, and 86 make a right triangle
    11·2 answers
  • Solve this system of equations to find x and y, please, and explain how you did it:
    7·1 answer
  • Yesterday was the 13th. If the day after tomorrow is Wednesday, what will the date be on Saturday?
    8·2 answers
  • Which of the following is the lowest common denominator for the fractions 5/6 and 3/4? A)4 B)12 C)15 D)24
    7·1 answer
  • What is the name of the relationship between angle 5 and angle 7?<br> PleSe help
    6·1 answer
  • Plz help me this is to much
    9·1 answer
  • Find the measure of angle x. Please helpp
    15·1 answer
  • Find the value of m​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!