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
vodka [1.7K]
3 years ago
6

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true

standard deviation .75. a. Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 4.85. b. Compute a 98% CI for true average porosity of another seam based on 16 specimens with a sample average porosity of 4.56.
Mathematics
1 answer:
IgorLugansk [536]3 years ago
7 0

Answer:

(a) 95% confidence interval for the true average porosity of a certain seam is [4.52 , 5.18].

(b) 98% confidence interval for the true average porosity of a another seam is [4.12 , 4.99].

Step-by-step explanation:

We are given that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.75.

(a) Also, the average porosity for 20 specimens from the seam was 4.85.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

                      P.Q. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample average porosity = 4.85

            \sigma = population standard deviation = 0.75

            n = sample of specimens = 20

            \mu = true average porosity

<em>Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.</em>

<u>So, 95% confidence interval for the true mean, </u>\mu<u> is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                     of significance are -1.96 & 1.96}  

P(-1.96 < \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < 1.96) = 0.95

P( -1.96 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X-\mu} < 1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

P( \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

<u>95% confidence interval for</u> \mu = [ \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ]

                                            = [ 4.85-1.96 \times {\frac{0.75}{\sqrt{20} } } , 4.85+1.96 \times {\frac{0.75}{\sqrt{20} } } ]

                                            = [4.52 , 5.18]

Therefore, 95% confidence interval for the true average porosity of a certain seam is [4.52 , 5.18].

(b) Now, there is another seam based on 16 specimens with a sample average porosity of 4.56.

The pivotal quantity for 98% confidence interval for the population mean is given by;

                      P.Q. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample average porosity = 4.56

            \sigma = population standard deviation = 0.75

            n = sample of specimens = 16

            \mu = true average porosity

<em>Here for constructing 98% confidence interval we have used One-sample z test statistics as we know about population standard deviation.</em>

<u>So, 98% confidence interval for the true mean, </u>\mu<u> is ;</u>

P(-2.3263 < N(0,1) < 2.3263) = 0.98  {As the critical value of z at 1% level

                                                   of significance are -2.3263 & 2.3263}  

P(-2.3263 < \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < 2.3263) = 0.98

P( -2.3263 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X-\mu} <  2.3263 ) = 0.98

P( \bar X-2.3263 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+2.3263 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.98

<u>98% confidence interval for</u> \mu = [ \bar X-2.3263 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+2.3263 \times {\frac{\sigma}{\sqrt{n} } } ]

                                            = [ 4.56-2.3263 \times {\frac{0.75}{\sqrt{16} } } , 4.56+2.3263 \times {\frac{0.75}{\sqrt{16} } } ]

                                            = [4.12 , 4.99]

Therefore, 98% confidence interval for the true average porosity of a another seam is [4.12 , 4.99].

You might be interested in
Marsha uses 8.5 pints of white paint and blue paint to paint her bedroom walls. 2/5
Serjik [45]

Answer:

5.1 pints

Step-by-step explanation:

Theres 2 ways

First way:

We can do 2/5 of 8.5 which is 3.4. Then, we can subtract 3.4 from 8.5 and get 5.1 pints.

Second way:

We can simply do 3/5 of 8.5 because the remaining 3/5 of the paint is blue. 3/5 of 8.5 is 5.1 pints

Hope this helped! I would appreciate a Brainliest if this helped you!

6 0
2 years ago
Please help me fast! I will give brainly
Afina-wow [57]

Answer:

He's correct.

Step-by-step explanation:

As long as there is no change in sign of the variables.

8 0
3 years ago
Read 2 more answers
How do i simplify 3√96×√98
Vera_Pavlovna [14]
<span>3√96 * √98 = </span><span>12√6 * 7√2 = 84</span>√12 = 168√3
5 0
3 years ago
What is the distance between the points (4,-2) and )-5,3)?
abruzzese [7]

Answer:

10.3

Step-by-step explanation:

Let the given points be the endpoints of a right triangle.  The horizontal change in x is from 4 to -5 and is negative 9; the vertical change in y is from -2 to+ 3 and is +5.

The desired distance is found using the Pythagorean theorem:

d = √(9² + 5²) = √106, or 10.3 (to the nearest tength)

3 0
3 years ago
X+y=0.5<br> x-y=1<br> elimination meathod
user100 [1]

Answer:

x=0.75, y=-0.25

Step-by-step explanation:

We can add the two equations to eliminate y and solve for x.

x+y+x-y=0.5+1

2x=1.5

x=0.75

Now, we can find for y by using substitution:

x+y=0.5 (given)

0.75+y=0.5

y=-0.25

Hope this helps :)

8 0
3 years ago
Other questions:
  • What is the ordered pair for point K?
    8·2 answers
  • Help with any of the questions please!
    8·1 answer
  • <img src="https://tex.z-dn.net/?f=%20%5Clim_%7B%28x%2Cy%29%20%5Cto%20%5C%20%280%2C0%29%7D%20%28x%5E4%20%2By%5E3%29%2F%28x%5E4%20
    11·1 answer
  • Pls help! answer will get brainliest
    7·1 answer
  • Find the of this circle in terms of pi
    14·2 answers
  • Xzavion buys 1.2 pounds of strawberries. If each pound of strawberries cost $3.70, how much will he pay for the strawberries?
    6·2 answers
  • 4(x-7)=2(x+3) solve for x
    13·2 answers
  • WILL MARK BRAINLIEST IF GOTTEN RIGHT! DONT ANSWER IF U DONT KNOW!
    12·2 answers
  • 4) What is the domain of the function?<br> Please help
    5·1 answer
  • 12. For which of the following quadratic equations are the roots 2 and 57
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!