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
svetoff [14.1K]
3 years ago
11

Two machines are used for filling glass bottles with a soft-drink beverage. The filling process have known standard deviations s

igma(1) = 0.010 liter and sigma(2) = 0.015 liter, respectively. A random sample of n(1) = 25 bottles from machine 1 and n(2) = 20 bottles from machine 2 results in average net contents of x-bar = 2.04 liters and x-bar = 2.07 liters.
(a) Test the hypothesis that both machines fill to the same net contents, using alpha = 0.05. What are your conclusions?
(b) Find the P-value for this test.
(c) Construct a 95% confiedence interval on the difference in mean fill volume.
Mathematics
1 answer:
stellarik [79]3 years ago
8 0

Answer:

a. We reject the null hypothesis at the significance level of 0.05

b. The p-value is zero for practical applications

c. (-0.0225, -0.0375)

Step-by-step explanation:

Let the bottles from machine 1 be the first population and the bottles from machine 2 be the second population.  

Then we have n_{1} = 25, \bar{x}_{1} = 2.04, \sigma_{1} = 0.010 and n_{2} = 20, \bar{x}_{2} = 2.07, \sigma_{2} = 0.015. The pooled estimate is given by  

\sigma_{p}^{2} = \frac{(n_{1}-1)\sigma_{1}^{2}+(n_{2}-1)\sigma_{2}^{2}}{n_{1}+n_{2}-2} = \frac{(25-1)(0.010)^{2}+(20-1)(0.015)^{2}}{25+20-2} = 0.0001552

a. We want to test H_{0}: \mu_{1}-\mu_{2} = 0 vs H_{1}: \mu_{1}-\mu_{2} \neq 0 (two-tailed alternative).  

The test statistic is T = \frac{\bar{x}_{1} - \bar{x}_{2}-0}{S_{p}\sqrt{1/n_{1}+1/n_{2}}} and the observed value is t_{0} = \frac{2.04 - 2.07}{(0.01246)(0.3)} = -8.0257. T has a Student's t distribution with 20 + 25 - 2 = 43 df.

The rejection region is given by RR = {t | t < -2.0167 or t > 2.0167} where -2.0167 and 2.0167 are the 2.5th and 97.5th quantiles of the Student's t distribution with 43 df respectively. Because the observed value t_{0} falls inside RR, we reject the null hypothesis at the significance level of 0.05

b. The p-value for this test is given by 2P(T0 (4.359564e-10) because we have a two-tailed alternative. Here T has a t distribution with 43 df.

c. The 95% confidence interval for the true mean difference is given by (if the samples are independent)

(\bar{x}_{1}-\bar{x}_{2})\pm t_{0.05/2}s_{p}\sqrt{\frac{1}{25}+\frac{1}{20}}, i.e.,

-0.03\pm t_{0.025}0.012459\sqrt{\frac{1}{25}+\frac{1}{20}}

where t_{0.025} is the 2.5th quantile of the t distribution with (25+20-2) = 43 degrees of freedom. So

-0.03\pm(2.0167)(0.012459)(0.3), i.e.,

(-0.0225, -0.0375)

You might be interested in
What is -(x - 8) simplified?
expeople1 [14]
You really can’t simply it but if u use disruptive property it would be -x - -8
5 0
2 years ago
(a) Describe a property specific to squares that is not a property specific to rectangles.
blondinia [14]

Answer:

Step-by-step explanation:

(a) A square has all the 4 sides being equal while a rectangle has four sides, with the opposite sides being parallel and the same length.

(b) The diagonals bisect the angles , the diagonals are perpendicular bisectors of each other

(c) A square has two pairs of parallel sides, four right angles, and all four sides are equal while the angles of a parallelogram are not right angles

(d) a rhombus can be a rectangle (if the angles of the rhombus are all 90 degrees), and a rectangle can be a rhombus (if the sides of the rectangle are all equal length). Opposite sides are parallel.

(e) a rhombus has two opposite internal angles of equal measure, a square has four right angles with equal measure

5 0
3 years ago
Read 2 more answers
The campsite shop sells boxes of Funshine Cereal.
irga5000 [103]
The boxes are kept is 2275 cm and the boxes 10800 mm
3 0
3 years ago
Solve the system of equations. \begin{aligned} &amp; -5x+13y = -7 \\\\ &amp; 5x+4y=24 \end{aligned} ​ −5x+13y=−7 5x+4y=24 ​ x= e
riadik2000 [5.3K]

Answer:

The solution of the given equations

x =4 , y = 1

Step-by-step explanation:

<u>Explanation</u>:-

<u>Step(l</u>):-

Given the system of equations -5x+13y = -7 ..(l)

                                                     5x+4y=24 ..(ll)

<u>Step(ll)</u>

Adding (l) and (ll) equations and cancelling '5x' terms we get

         13y+4y = -7 +24

               17y = 17

dividing '17' on both sides, we get

                y=1

<u>Step(lll):-</u>

Substitute y=1 in equation (l) , we get

-5x+13y = -7

-5x + 13(1) = -7

subtracting '13' on both sides, we get

-5x +13 -13= -7 -13

-5x = -20

Dividing '-5' on  both sides, we get

x = \frac{-20}{-5}

x = 4

<u>Conclusion</u>:-

The solution of the given equations

x =4 , y = 1

7 0
3 years ago
How many solutions does the equation have? 4(2n−4)+3=8n−19
kondaur [170]
Are there answers? I would love to help more :)

6 0
3 years ago
Read 2 more answers
Other questions:
  • The volume of a shampoo filled into a container is uniformly distributed between 370 and 385 milliliters. (a) What are the mean
    15·1 answer
  • Simplify the expression. Justify that the expressions are equivalent using x = 2. –4(5x + 2) – 6(x – 3) What is the simplified e
    7·2 answers
  • 4%of 100 is the same as 8% of what number? explain how you arrived at your answer.
    8·2 answers
  • Match the equation on the left with its solution(s) on the right.
    14·1 answer
  • Y= x^2 -5 solve for x
    11·1 answer
  • Find the midpoint of the line segment.
    6·1 answer
  • Find the area of the trapezoid. If the answer is not an integer, leave it in simplest radical form. The figure is not to scale.
    14·1 answer
  • Help a girl out once again ? <br><br> Have a great day !!!!
    7·1 answer
  • Solve, correct people get brainliest
    5·2 answers
  • At a store Ron bought two shirts of same price and a neck-tie for $90. At the same store, on the same day, Bruce paid $12 for th
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!