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
PSYCHO15rus [73]
3 years ago
12

Use the information provided to determine a 95% confidence interval for the population variance. A researcher was interested in

the variability in service time (in hours) spent by mechanics fixing the same automotive problem. A random sample was taken resulting in a sample of size 20 from a substantial file of reported experience. The summary statistics are as follows: n = 20, sample mean = 13.8 hours, sample standard deviation = 3.9 hours. Assume service time follows a normal distribution. Round to two decimal places.

Mathematics
1 answer:
Leno4ka [110]3 years ago
4 0

Answer:

The 95% confidence interval for the population variance is (8.80, 32.45).

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for the population variance is given as follows:

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

It is provided that:

<em>n</em> = 20

<em>s</em> = 3.9

Confidence level = 95%

⇒ <em>α</em> = 0.05

Compute the critical values of Chi-square:

\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.05/2, (20-1)}=\chi^{2}_{0.025,19}=32.852\\\\\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{1-0.05/2, (20-1)}=\chi^{2}_{0.975,19}=8.907

*Use a Chi-square table.

Compute the 95% confidence interval for the population variance as follows:

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

\frac{(20-1)\cdot (3.9)^{2}}{32.852}\leq \sigma^{2}\leq \frac{(20-1)\cdot (3.9)^{2}}{8.907}\\\\8.7967\leq \sigma^{2}\leq 32.4453\\\\8.80\leq \sigma^{2}\leq 32.45

Thus, the 95% confidence interval for the population variance is (8.80, 32.45).

You might be interested in
Two pounds of peaches cost $4.20. How much will five pounds cost?
Dimas [21]
Set up multiplication of ratios so that they cancel out units that you do not need in your final answer...

5lb($4.20/2lb)=$10.50
8 0
3 years ago
Read 2 more answers
Solve 2x+7=x-3 Please can u show your working out
Korolek [52]
X= -10
You may review the image Ive attached to see how I got this answer.

7 0
3 years ago
Read 2 more answers
Please help if i get this wrong i will fail
LUCKY_DIMON [66]
The answer is either b or c
3 0
3 years ago
Read 2 more answers
HELP NEEDED ASAP I’m gonna fail math if I don’t get help lol
sergiy2304 [10]

Answer:

I think that -0.0000002 is the least, but I don't know the rest. I hope you can find the rest though. Happy Holidays!

Step-by-step explanation:

3 0
3 years ago
Is 10.846 an integer ​
yulyashka [42]

Hello!

An integer is defined as a number which is not a fraction or irrational. It should be able to be written out as just a number, without a decimal point or additional fraction. (It can have a negative sign) For example, a few integers would be 2, 5, -8, and 9109, while some non-integers would be 3.1, 3 3/2, and 5i.

In this case, 10.846 is not an integer, as it has a decimal.

Hope this helps!

3 0
3 years ago
Other questions:
  • Someone plz answer this for me
    9·1 answer
  • Can someone help :-)
    8·1 answer
  • Factor x^2-6x+9 &lt;&lt;&lt; Need Help?
    8·2 answers
  • Replace ∗ with a monomial so that the expression can be rewritten as a square of a sum or a difference:
    10·1 answer
  • Find the value of x in this proportion.<br> (x+3)<br> O 27/4<br> 018<br> Ö9/8<br> © 9/2
    14·1 answer
  • Help please? Find the values of a,b,c,d,e and f
    13·1 answer
  • 3a. The graph shows a school's profit P for selling x lunches on one day. PART A: What is the school's profit for selling 120 lu
    14·2 answers
  • The Utica Boilermaker is a 15-kilometer road race. Sara is signed up
    11·1 answer
  • Algebra- pls help ;-;<br> will mark brainliest
    13·2 answers
  • Where will the hand of a clock stop if it start at 2 and make 1 by 4 of a Revolution clockwise​
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!