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
devlian [24]
2 years ago
11

You work for a soft-drink company in the quality control division. You are interested in the standard deviation of one of your p

roduction lines as a measure of consistency. The product is intended to have a mean of 12 ounces, and your team would like the standard deviation to be as low as possible. You gather a random sample of 15 containers. Estimate the population standard deviation at a 98% level of confidence.
12.05 12 11.96 12.14 12.12
11.97 11.96 12.11 11.94 11.82
12 12.18 11.91 12.06 11.99

(Data checksum: 180.21)

Note: Keep as many decimals as possible while making these calculations. If possible, keep all answers exact by storing answers as variables on your calculator or computer.

a) Find the sample standard deviation:

b) Find the lower and upper χ2χ2 critical values at 98% confidence:
Lower: Upper:

c) Report your confidence interval for σσ: ( , )
Mathematics
1 answer:
frutty [35]2 years ago
3 0

Answer:

Step-by-step explanation:

weight (x)                         ( x - \overline x)^2

12.05                               0.00123

12                                     0.00019

11.96                                0.00292

12.14                                0.0159

12.12                                0.00112

11.97                                0.0019

11.96                               0.0029

12.11                                 0.0092

11.94                                 0.0055

11.82                                0.038

12                                     0.00019

12.18                                0.028

11.91                                  0.0108

12.06                                0.0021

11.99                                  0.0029

\sum x = 180.21                    \sum (x - \overline x)^2 = 0.12285

Sample size = 15

\overline x = \dfrac{180.21}{15} = 12.014

Sample standard deviation

x = \sqrt{\dfrac{0.12285}{15-1}}

x = 0.0937

\text{degree of freedom = n - 1}

degree of freedom = 15- 1=14

\text{confidence interval} \alpha = 1- 0.98 = 0.02 \\ \\ \alpha/2 = 0.02/2 = 0.01

From \  X^2  \  table}\text{, the critical value} X^2 \text{=0.99 for degree of freedom =14 is given by : 4.660}

\text{, the critical value} X^2 \text{=0.01 for degree of freedom =14 is given by : 29.141}

\text{Thus, the lower limit = 4.660, the upper limit = 29.141}

\text{the confidence interval of the standard deviation} \ \sigma \  is:

\sqrt{\dfrac{(n -1)s^2}{X^2_{\dfrac{\sigma}{2}}} } \le \sigma \le \sqrt{\dfrac{(n -1)s^2}{X^2_{1-\dfrac{\sigma}{2}}} }

replacing our values:

\sqrt{\dfrac{(15 -1)0.0937^2}{29.141} } < \sigma

= 0.06495 < \sigma < 0.1624

\mathbf{Thus; \  \sigma (0.06495 , 0.1624)}

You might be interested in
What are the steps for constructing a circumscribed circle for using only a compass and a straightedge?
Marta_Voda [28]
Construct the perpendicular bisector of one side of triangle
Construct the perpendicular bisector of another side
Where they cross is the center of the Circumscribed circle
Place compass on the center point, adjust its length to reach any corner of the triangle, and draw your Circumscribed circle!
4 0
3 years ago
Read 2 more answers
I mark brianlest just help me;-;
Rina8888 [55]

Answer:

B)113.04 cm^2

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Which property is used to write a(x + y) = ax + ay
stealth61 [152]
The Distributive Property. You are distributing a to x + y.

Hope this helps!
3 0
3 years ago
Read 2 more answers
Do you like my drawing
rosijanka [135]

Answer:

yes!!!

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
The exterior angle measure of a regular polygon is 20 degrees. How many sides does the polygon have? 9 16 18 20
notka56 [123]
The polygon would have 18 sides. Hope this helps!
8 0
3 years ago
Read 2 more answers
Other questions:
  • Suppose the U. S. president wants an estimate of the proportion of the population who support his current policy toward revision
    15·1 answer
  • Which polynomial is in standard form?
    5·1 answer
  • Kim's softball team was playing in the championship game. When there were
    8·1 answer
  • What type of organism is able to cause an infection?
    13·2 answers
  • Lee and Jessie swam towards each other from opposite sides of a lake that is 3.9km wide. They began swimming at 2:00 P.M. and me
    15·1 answer
  • Mary wants to find this product. 58 x 20 How can Mary find the product? A. 0 +16 + 100 B. 0 + 160 + 1000 . C. 58 + 16 + 100 D. 5
    9·1 answer
  • What is m∠1?.........
    5·2 answers
  • Kendra has $32 and is planning to save $25 each week. She is saving to buy a new phone that costs $257.00. Write an equation to
    7·1 answer
  • Francisco makes $11 per hour doing part time work on Saturdays. He spends $3 on transportation to and from work. The equation y
    5·2 answers
  • What is two less than the quotient of 25 and 5
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!