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
Write the answer in numeric form?
kondor19780726 [428]

Answer:

x=11. 38 degrees; 52 degrees

Step-by-step explanation:

90+6x-14+3x+5=180

81+9x=180

9x=99

x=11

38 degrees, 52 degrees

8 0
3 years ago
Ocean waves and electromagnetic waves
o-na [289]

Answer:

true they are similar

3 0
3 years ago
Read 2 more answers
Sean has 1/5 of a cupcake and 1/5 of a large cake. Does the sum 1/5 + 1/5 make sense in this situation
svetlana [45]

Answer:

The size of the cupcake and the size of the cake differ, so when your saying 1/5 of the cupcake, 1/5 of a cupcake is not the same as 1/5 of the cake . Idk if this will help, but I gave you a suggestion!

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Is 5,280 yards greater than 1 mile
Novay_Z [31]
Yes, there is 1760 yards in a mile.
5 0
3 years ago
Read 2 more answers
Given that the domain is all real numbers, what is the limit of the range for the function ƒ(x) = 4^2x - 100?
andreev551 [17]
[ -100, ∞ ). as X decreases f of x approaches -100 asymptotically as X increases f of x increases without bound
7 0
3 years ago
Read 2 more answers
Other questions:
  • cream cheese costs £3.60 for 1kg. Robbie buys a pot of ice cream cheese for 90p. How many grams of cream cheese does he buy?
    5·2 answers
  • Quick help !!
    11·2 answers
  • Sam works as a waiter in a restaurant. He earns $1,400 per month as a base salary, plus tips averaging 15% of the meals he serve
    8·1 answer
  • How do u solve this problem “15 = 2 − 5?”
    11·2 answers
  • 2. Estimate the sum. Choose the mixed number that is closest to the estimate. 5.5 + 4.2
    7·1 answer
  • Julie runs 1 1/2 miles in 1/3 hour.How many miles will she run per hour at the same speed?
    10·1 answer
  • Y=6x +1<br> Function rule
    9·1 answer
  • 9+5(4x+4) how do I solve this problem?
    10·1 answer
  • Factor completely:<br> x^2-x^2-3.5(x+y)
    6·2 answers
  • The area of a rhombus is 72 m2. One<br> diagonal is 18m. Find the other diagonal.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!