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
Anton [14]
2 years ago
12

Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random

Mathematics
1 answer:
Katyanochek1 [597]2 years ago
7 0

Answer:

a) Null hypothesis: \mu_A =\mu_B =\mu C

Alternative hypothesis: \mu_i \neq \mu_j, i,j=A,B,C

SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 =20.5  

SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 =12.333  

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 =8.16667  

And we have this property  

SST=SS_{between}+SS_{within}  

The degrees of freedom for the numerator on this case is given by df_{num}=df_{within}=k-1=3-1=2 where k =3 represent the number of groups.

The degrees of freedom for the denominator on this case is given by df_{den}=df_{between}=N-K=3*6-3=15.

And the total degrees of freedom would be df=N-1=3*6 -1 =15

The mean squares between groups are given by:

MS_{between}= \frac{SS_{between}}{k-1}= \frac{12.333}{2}=6.166

And the mean squares within are:

MS_{within}= \frac{SS_{within}}{N-k}= \frac{8.1667}{15}=0.544

And the F statistic is given by:

F = \frac{MS_{betw}}{MS_{with}}= \frac{6.166}{0.544}= 11.326

And the p value is given by:

p_v= P(F_{2,15} >11.326) = 0.00105

So then since the p value is lower then the significance level we have enough evidence to reject the null hypothesis and we conclude that we have at least on mean different between the 3 groups.

b) (\bar X_B -\bar X_C) \pm t_{\alpha/2} \sqrt{\frac{s^2_B}{n_B} +\frac{s^2_C}{n_C}}

The degrees of freedom are given by:

df = n_B +n_C -2= 6+6-2=10

The confidence level is 99% so then \alpha=1-0.99=0.01 and \alpha/2 =0.005 and the critical value would be: t_{\alpha/2}=3.169

The confidence interval would be given by:

(43.333 -41.5) - 3.169 \sqrt{\frac{0.6667}{6} +\frac{0.7}{6}}= 0.321

(43.333 -41.5) + 3.169 \sqrt{\frac{0.6667}{6} +\frac{0.7}{6}}=3.345

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

Part a  

Null hypothesis: \mu_A =\mu_B =\mu C

Alternative hypothesis: \mu_i \neq \mu_j, i,j=A,B,C

If we assume that we have 3 groups and on each group from j=1,\dots,6 we have 6 individuals on each group we can define the following formulas of variation:  

SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 =20.5  

SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 =12.333  

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 =8.16667  

And we have this property  

SST=SS_{between}+SS_{within}  

The degrees of freedom for the numerator on this case is given by df_{num}=df_{within}=k-1=3-1=2 where k =3 represent the number of groups.

The degrees of freedom for the denominator on this case is given by df_{den}=df_{between}=N-K=3*6-3=15.

And the total degrees of freedom would be df=N-1=3*6 -1 =15

The mean squares between groups are given by:

MS_{between}= \frac{SS_{between}}{k-1}= \frac{12.333}{2}=6.166

And the mean squares within are:

MS_{within}= \frac{SS_{within}}{N-k}= \frac{8.1667}{15}=0.544

And the F statistic is given by:

F = \frac{MS_{betw}}{MS_{with}}= \frac{6.166}{0.544}= 11.326

And the p value is given by:

p_v= P(F_{2,15} >11.326) = 0.00105

So then since the p value is lower then the significance level we have enough evidence to reject the null hypothesis and we conclude that we have at least on mean different between the 3 groups.

Part b

For this case the confidence interval for the difference woud be given by:

(\bar X_B -\bar X_C) \pm t_{\alpha/2} \sqrt{\frac{s^2_B}{n_B} +\frac{s^2_C}{n_C}}

The degrees of freedom are given by:

df = n_B +n_C -2= 6+6-2=10

The confidence level is 99% so then \alpha=1-0.99=0.01 and \alpha/2 =0.005 and the critical value would be: t_{\alpha/2}=3.169

The confidence interval would be given by:

(43.333 -41.5) - 3.169 \sqrt{\frac{0.6667}{6} +\frac{0.7}{6}}= 0.321

(43.333 -41.5) + 3.169 \sqrt{\frac{0.6667}{6} +\frac{0.7}{6}}=3.345

You might be interested in
Order the numbers 0.64, 2/3 , 65%, and 7/10 from least to greatest.
GalinKa [24]
2l3 , 7l10 , 0.64 , 65%
7 0
3 years ago
Read 2 more answers
Which statement explains how the lines x+y=2 and y=x+4 are related?
Basile [38]

Answer:

(2)They are perpendicular.

Step-by-step explanation:

3 0
3 years ago
Sam read 20% of the book on Monday and 0.2 of the book on Tuesday. If he read 50% of the remainder on Wednesday and still had 36
KonstantinChe [14]
Okay first you need to convert 0.2 to a percentage which would be 20% then 20% + 20% = 40% then it says he read 50%, 50% of 36 means that you have to multiply 36 two times to get, 72 then you do 72 * 40% = 28.8 = 29 + 72 = 101 pages in all then 101- 40%= 60.6 is how many pages were read on Monday and Tuesday.
8 0
3 years ago
Is (-4, 2) a solution of 4x + 5y < -7?
cupoosta [38]

Answer:

No

Step-by-step explanation:

Substitute the coordinates of the point into the left side of the inequality, evaluate and compare.

4(- 4) + 5(2) = - 16 + 10 = - 6 > - 7

Thus (- 4, 2 ) is not a solution

4 0
3 years ago
Sandra is making decorations for the school dance out of construction paper. Each decoration uses 223 2 2 3 sheets of paper. San
scoundrel [369]

Answer:

Step-by-step explanation:

CACA POOP

7 0
3 years ago
Other questions:
  • a student ran out of time on a multiple choice exam and randomly guess the answers for two problems each problem had 5oz choices
    5·2 answers
  • What is the inequality that represents the range of the function g(x)=-3/4x^2 when the domain is restricted to -4
    9·1 answer
  • The similarities and differences between correlation and regression Correlation and regression are two closely related topics in
    6·1 answer
  • CAN SOMEONE HELP ME ASAP THANK YOU SO MUCH :{
    10·1 answer
  • Kendall has 63 stickers. Her sister has 57 stickers.how many more stickers does Kendall have than her sister
    9·2 answers
  • 29, 19, 9, -1, ... <br> please help me out;(
    6·2 answers
  • What is the square root of 138
    14·2 answers
  • Which table represents a linear function? A two-column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. T
    6·2 answers
  • Jayden deposited $7100 in a savings account with simple interest. Three months later, the account held $7,259.75. what was the i
    14·1 answer
  • 8 teams dived 23 pizzas equally
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!