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ivanzaharov [21]
2 years ago
14

A table titled Text messages sent has 25 entries.

Mathematics
1 answer:
Studentka2010 [4]2 years ago
5 0
This is uselful! Thanks: ))
You might be interested in
Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random
Katyanochek1 [597]

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

7 0
3 years ago
Find the x intercept and y intercept of -5x-40=y
nataly862011 [7]

Answer:

2

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
I WILL MARK AS BRAINLIST The quantities x and y are proportional Find the constant of proportionality (r) in the equation y=rx
tekilochka [14]

Answer:

\frac{1}{2}

Step-by-step explanation:

Given that x and y are proportional and the equation relating them is

y = rx ← r is the constant of proportionality

To find r use any ordered pair from the table

Using x = 9, y = 4.5 , then

4.5 = 9r ( divide both sides by 9 )

\frac{4.5}{9} = r , that is

r = \frac{1}{2}

7 0
3 years ago
Read 2 more answers
Find the surface area of the rectangle prism. 3cm 9cm and 6cm
lisabon 2012 [21]

Answer:

198 cm²

Step-by-step explanation:

We are given the dimensions of a rectangular prism;

3cm 9cm and 6cm

We are required to determine its surface area;

We need to know that;

Surface area of a rectangular prism is given by;

A = 2(WL+HL+WH)

Where L, W and H are length , width and height respectively;

Assuming;

Width is 3 cm

Length is 9 cm, and

Height is 6 cm

Then;

Area = 2 ( (3×9) + (6×9) + (3×6))

        = 2(99)

       = 198 cm²

Therefore, the area of the rectangular prism is 198 cm²

6 0
3 years ago
Students in a college statistics class want to conduct a survey to determine the percentage of students in the school who are wi
valentina_108 [34]

Answer:

d.a cluster sampling

Step-by-step explanation:

This plan exemplifies Cluster sampling. It is a sampling method where populations are placed into different separate groups like here into freshman, sophomore, junior, and senior classes. A random sample of these groups is then selected as here thirty students selected from each group to represent a specific population.<u> It is usually used in that type of research when there is no possible way to find information about a population as a whole.</u>

4 0
3 years ago
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