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
alexgriva [62]
3 years ago
13

A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population. The chi-square val

ues to be used for this interval estimation are
a. 16.151 and 40.113.

b. 14.573 and 43.195.

c. 15.308 and 44.461.

d. 11.808 and 49.645.
Mathematics
1 answer:
Natali5045456 [20]3 years ago
7 0

Answer:

\chi^2_{\alpha/2}=43.195

\chi^2_{1- \alpha/2}=14.573

b. 14.573 and 43.195.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi square distribution is the distribution of the sum of squared standard normal deviates .

2) Solution to the problem

The confidence interval for the population variance is given by the following formula:

\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}

We need on this case to calculate the critical values. First we need to calculate the degrees of freedom given by:

df=n-1=28-1=27

Since the Confidence is 0.95 or 95%, the value of \alpha=1-0.95=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table for the Chis square distribution with 27 degrees of freedom to find the critical values. We need a value that accumulates 0.025 of the area on the left tail and 0.025 of the area on the right tail.  

The excel commands would be: "=CHISQ.INV(0.025,27)" "=CHISQ.INV(0.975,27)". so for this case the critical values are:

\chi^2_{\alpha/2}=43.195

\chi^2_{1- \alpha/2}=14.573

b. 14.573 and 43.195.

You might be interested in
Find the value of k by<br>quardractic equation two real and equal roots<br>5x - 2kx +20=0​
kotegsom [21]

Answer:

k = +10 or -10

Step-by-step explanation:

It's given in the question that the roots of the eqn. are real and equal. So , the discriminant of the eqn. should be equal to 0.

=  >  {b}^{2}  - 4ac = 0

=  >  {( - 2k)}^{2}  - 4 \times 5 \times 20 = 0

=  > 4 {k}^{2}  - 400 = 0

=  > 4( {k}^{2}  - 100) = 0

=  >  {k}^{2}  - 100 = 0

=  > k =  \sqrt{100}  =  + 10 \: or \:  - 10

3 0
3 years ago
Read 2 more answers
A triangle has an area of 230.86 square inches.the height of the triangle is 23.8 inches .what is the length of the base of the
Annette [7]

Answer:

The length of the base of the triangle is 19.4 inches.

7 0
2 years ago
PLEASE HELP ME
patriot [66]
What grade jeiiieudhwhwjskjewhehkzbzvdvs
5 0
2 years ago
Read 2 more answers
John has $400. He gave one friend 25% and $158.67 to another friend. How much money does John have left​
sdas [7]

Answer:

$141.33

Step-by-step explanation:

He gave $100 to one fried and 158.67 to another

100+158.67=258.67

5 0
3 years ago
Read 2 more answers
You sign up for a movie plan that costs $12 per month. You get the first 2 months free. If you use the plan for 24 months, how m
alexandr1967 [171]
You are going to pay for a total of 22 months, so the answer will be 12*22.  This equals $264, or the first option.
7 0
3 years ago
Other questions:
  • Suppose the students construct a 95% confidence interval for the true weight of their rocks. Whose interval do you expect to be
    6·1 answer
  • 3. Leo made a container to store his camping gear. The container is in the shape of a rectangular prism. The container has mater
    14·1 answer
  • A circle has the equation (x-2)^2 +y^2 =5. What are the coordinates of the circle's center?
    6·1 answer
  • 1 x 0 = 0?
    11·2 answers
  • A composition of two isometries results in __________.
    7·2 answers
  • Change ratio to actual numbers
    11·2 answers
  • For each system of equations, drag the true statement about its solution set to the box
    7·1 answer
  • Write an inequality to respresent the situation.
    10·1 answer
  • I need help pleaseee
    12·1 answer
  • What is cos (A)?<br> Pls help!!
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!