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
aleksklad [387]
3 years ago
7

A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked t

o indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow.
Age Group
Hours of Sleep 39 or younger 40 or older
Fewer than 6 38 36
6 to 6.9 61 58
7 to 7.9 76 74
8 or more 65 92
(a) Conduct a test of independence to determine whether hours of sleep are independent of age.
(b) What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night?
Mathematics
1 answer:
alekssr [168]3 years ago
7 0

Answer:

Sleep hours per night is independent.

Step-by-step explanation:

Given the data:

Hours of Sleep 39 or younger 40 or older

> 6 _____38 36

6 to 6.9 _ 61 58

7 to 7.9 __76 74

8 or more 65 92

The Chisquare statistic is to be used to perform the analysis :

The hypothesis :

H0: Sleep hours per night is independent

H1: Sleep hours per night is not independent

χ² = (observed - Expected)² / Expected

To save computation time. We could use a Chisquare calculator to perform the analysis :

The test statistic = 4.0061

The degree of freedom = (row - 1) * (column - 1)

Degree of freedom = (4-1)*(2-1) = 3*1 = 3

The Pvalue = 0.261

Since, Pvalue > α ; We fail to reject the H0 ;and conclude that sleep hours per night is independent.

______________total ___%

> 6 _____38 36__ 74 __ 14.8

6 to 6.9 _ 61 58 __ 119 __23.8

7 to 7.9 __76 74___150__30

8 or more 65 92___157__31.4

_______240 _260__500_100

You might be interested in
In three more years, Angelo’s grandfather will be six times as old as Angelo was last year. When
Katen [24]
You can give me the choices, are there even any?

5 0
3 years ago
The square below represents one whole. Express the shaded area as a fraction, a decimal, and a percent of the whole.
lozanna [386]

Answer as a fraction = 1/2

Answer as a decimal = 0.5

Answer as a percent = 50%

========================================

Explanation:

There are 5 blue rectangles out of 10 total. This forms the fraction 5/10 and that reduces to 1/2 after dividing both parts by 5. Therefore, the fractions 5/10 and 1/2 are the same. Notice that exactly half of the entire figure is shaded blue.

Use long division or your calculator to find that 1/2 = 0.5 which converts to 50% when you move the decimal point 2 spots to the right.

8 0
3 years ago
Read 2 more answers
The rate at which a quantity of a radioactive substance decays is proportional to the quantity of the substance. The constant of
Butoxors [25]

Answer:

\frac{dN}{dt} = λN           N(0) = 6

N(t) = N₀e^(λt)

Applying the inital value condition

N(t) = 6e^(λt)

Step-by-step explanation:

Summarizing  the information briefly and stating the  variables in the problem.

t = time elapsed during the decay

N(t) = the amount of the radioactive substance remaining after time t

λ= The constant of proportionality  is called the decay constant or decay rate

Given the initial conditions

N(0) = N₀ = 6

The rate at which a quantity of a radioactive substance decays (\frac{dN}{dt}) is proportional to the quantity of the substance (N)  and λ is the constant of proportionality  is called the decay constant or decay rate :

\frac{dN}{dt} = λN          

N(t) = N₀e^(λt) ......equ 1

substituting the value of  N₀ = 6 into equation 1

N(t) = 6e^(λt)

3 0
3 years ago
Debbie scored of her team's 24 points. How<br>many points did Debbie score?​
olga55 [171]

Answer:

24

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
The length of a rectangle is 16 feet more than three times the width. The perimeter of the rectangle is 248 feet. Find the dimen
sattari [20]

Answer:

L = 97, w = 27

Step-by-step explanation:

The perimeter formula is P = 2L + 2w.  We have too many unknowns simply to plug in, so we have to find a way to identify one in terms of the other.  The statement is that the length is 16 feet more than 3 times the width, so the length is in terms of the width and can be identified as

L = 3w + 16

and the width, then, is just w.  Now we can fill in those 2 values, both in terms of w, and set it to equal the perimeter value we were given of 248:

2(3w + 16) + 2w = 248 and

6w + 32 + 2w = 248 and

8w + 32 = 248 and

8w = 216 so

w = 27

That means that the width is 27.  Use that value of w now to find the length where

L = 3w + 16.

L = 3(27) + 16 and

L = 97

6 0
3 years ago
Other questions:
  • For the pair of functions, find the indicated sum, difference, product, or quotient. f(x) = 16 - x2; g(x) = 4 - x Find (f + g)(x
    9·2 answers
  • The arithmetic mean of two numbers is 18 and the geometric mean is 16. find the sum of squares of the numbers
    8·1 answer
  • Evaluate the limit by first recognizing the sum as the Riemann sum for a function defined on the interval [0,1]: lim as n approa
    15·1 answer
  • Use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern. –9, –4, 1, 6, . . .
    5·2 answers
  • How many triangles can be constructed with angles measuring 25º, 25º, and 130º? A. one B.none C.more than one
    13·2 answers
  • Big babies: The National Health Statistics Reports described a study in which a sample of 354 one-year-old baby boys were weighe
    13·1 answer
  • Please help me with this question:)!
    9·1 answer
  • How can you<br> change the equation y = mx + b to<br> shift the graph down?
    6·1 answer
  • Find the total surface area. Round to the nearest hundredth if necessary.
    15·1 answer
  • Identify the vertex, equation of the axis of symmetry, y-intercept, and zeros of the graph of a quadratic function.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!