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
Soloha48 [4]
3 years ago
13

A random sample of 9 wheels of cheese yielded the following weights in pounds has a sample mean of 20.90 and a sample variance o

f 3.45. Assume the weights of wheels of cheese have a normal distribution. Find a 90% confidence interval for the population variance.
Mathematics
1 answer:
Ronch [10]3 years ago
7 0

Answer:

2.002 \leq \sigma^2 \leq 11.365

Step-by-step explanation:

1) Data given and notation

s represent the sample standard deviation

s^2 represent the sample variance

n=9 the sample size

Confidence=90% or 0.90

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) Calculating the confidence interval

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

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

On this case we need to find the sample standard deviation with the following formula:

s=sqrt{\frac{\sum_{i=1}^9 (x_i -\bar x)^2}{n-1}}
The sample variance given was [tex]s^2=3.45

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

df=n-1=9-1=8

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical values.  

The excel commands would be: "=CHISQ.INV(0.05,8)" "=CHISQ.INV(0.95,8)". so for this case the critical values are:

\chi^2_{\alpha/2}=15.507

\chi^2_{1- \alpha/2}=2.732

And replacing into the formula for the interval we got:

\frac{(9)(3.45)}{15.507} \leq \sigma \frac{(9)(3.45)}{2.732}

2.002 \leq \sigma^2 \leq 11.365

You might be interested in
A 250-kVA, three-phase, 480-volt transformer requires 75 gallons of insulating oil to keep it properly cooled. How many liters i
Dennis_Churaev [7]

This problem can be directly solved by using a conversion factor. Simple research will tell us that 1 gallon contains about 3.78 Liter. Therefore the volume in Liter is:

volume = 75 gallons * (3.78 Liter / gallon)

<span>volume = 283.5 Liters</span>

7 0
3 years ago
A plumber has a 2.5 meter long copper pipe. He needs to cut lengths of 60cm,35cm and 90cm
Dima020 [189]
Hello.

The answer is 2315 cm.

To get the answer the equation is: 2500 - (60 +35 +90 )
To get 2500: 2.5 meters is 2500 cms
Then you would subtract how much he needs.

have a nice day
8 0
3 years ago
Examine the diagram.<br><br> What is the m
Phantasy [73]

Answer:

Step-by-step explanation:

Sum of all the angles of a triangle = 180°

∠A + ∠B + ∠C = 180°

48 + ∠B + 56 = 180

∠B  + 104 = 180

∠B = 180 - 104

∠B  = 76°

5 0
3 years ago
Read 2 more answers
24 students bought their permission slips to attend the class field trip to the local art museum. If this represented 8 tenths o
Sergio039 [100]

Answer:

30 in the class as total. 24/3= 8 30/3 =10

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
james scored 300 runs in cricket. he requires 900 runs to qualify for league MVP contention. he scores 50 runs during the averag
Serhud [2]
He would need to play 12 average scoring games.
900 (goal) - 300 (has) = 600
and 600/50 is 12 
hope this helps :)
5 0
3 years ago
Other questions:
  • How do you decide whether a number is a solution of an inequality
    10·1 answer
  • ermaine’s father owes $6,300 in interest at the end of a 60-month car loan at a 7% simple annual interest rate. What was the ori
    14·1 answer
  • Convert 12 over 5 to a decimal using long division.<br><br> 1.2<br><br> 2.4<br><br> 2.6<br><br> 3.4
    12·2 answers
  • 11/12+(−7/12). Write your answer as a fraction in simplest form.
    11·1 answer
  • Solve the proportional equation<br> 5/12 = x/15
    5·2 answers
  • NEED HELP EXPLAIN PLEASEEE
    15·1 answer
  • If f(x) = (ln x)^2, then f''( sqrt of e) is equal to _____.
    8·2 answers
  • 8x+2&gt;348 ,plezz i need help
    15·1 answer
  • Pls help me
    13·1 answer
  • PLEASE HELPPP!!!!
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!