Question

An executive at the home office of Big Rock Life Insurance is considering three branch managers...

An executive at the home office of Big Rock Life Insurance is considering three branch managers as candidates for promotion to vice president. The branch reports include records showing sales volume for each salesperson in the branch (in hundreds of thousands of dollars). A random sample of these records was selected for salespersons in each branch. All three branches are located in cities in which per capita income is the same. The executive wishes to compare these samples to see if there is a significant difference in performance of salespersons in the three different branches. If so, the information will be used to determine which of the managers to promote.

Branch Managed by Adams Branch Managed by McDale Branch Managed by Vasquez
7.4 8.6 6.9
6.6 10.9 8.3
10.3 11.3 10.5
11.2 9.6 11.8
9.7
10.2

Use a 1% level of significance. Shall we reject or not reject the claim that there are no differences among the performances of the salespersons in the different branches?

(a) What is the level of significance?


State the null and alternate hypotheses.

Ho: μ1 = μ2 = μ3; H1: Not all the means are equal.Ho: μ1 = μ2 = μ3; H1: All three means are different.    Ho: μ1 = μ2 = μ3; H1: At least two means are equal.Ho: μ1 = μ2 = μ3; H1: Exactly two means are equal.


(b) Find

SSTOT, SSBET, and SSW

and check that

SSTOT = SSBET + SSW.

(Round your answers to three decimal places.)

SSTOT

=

SSBET

=

SSW

=


Find

d.f.BET, d.f.W, MSBET, and MSW.

(Round your answers to three decimal places.)

d.f.BET

=

d.f.W

=

MSBET

=

MSW

=


Find the value of the sample F statistic. (Round your answers to three decimal places.)


What are the degrees of freedom?
(numerator)
(denominator)

(c) Find the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.001 < P-value < 0.010P-value < 0.001


(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P value is greater than the level of significance at α = 0.01, we do not reject H0.Since the P value is less than or equal to the level of significance at α = 0.01, we reject H0.    Since the P value is greater than the level of significance at α = 0.01, we reject H0.Since the P value is less than or equal to the level of significance at α = 0.01, we do not reject H0.


(e) Interpret your conclusion in the context of the application.

At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are all equal.    At the 1% level of significance there is insufficient evidence to conclude that the means are all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are not all equal.


(f) Make a summary table for your ANOVA test. (Round your answers to three decimal places.)

Source of
Variation
Sum of
Squares
Degrees of
Freedom
MS F
Ratio
P-Value Test
Decision
Between groups
Within groups
Total

Homework Answers

Answer #1

a)

level of significance =0.01

Ho: μ1 = μ2 = μ3; H1: Not all the means are equal

b)

SSTOT 37.384
SSBET 1.923
SSW 35.461
dfBET 2
dfW 11
MSBET 0.961
MSW 3.224
value of test statistic for factor A = 0.298
df(numerator) = 2
df(Denominator) = 11

c)

P-value > 0.100

d)

Since the P value is greater than the level of significance at α = 0.01, we do not reject H0.

e_)

At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal.

f_)

Source SS df MS F P value decision
Between 1.923 2 0.961 0.298 0.7480 fail to reject Ho
Within 35.461 11 3.224
Total 37.384 13
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
An executive at the home office of Big Rock Life Insurance is considering three branch managers...
An executive at the home office of Big Rock Life Insurance is considering three branch managers as candidates for promotion to vice president. The branch reports include records showing sales volume for each salesperson in the branch (in hundreds of thousands of dollars). A random sample of these records was selected for salespersons in each branch. All three branches are located in cities in which per capita income is the same. The executive wishes to compare these samples to see...
A random sample of companies in electric utilities (I), financial services (II), and food processing (III)...
A random sample of companies in electric utilities (I), financial services (II), and food processing (III) gave the following information regarding annual profits per employee (units in thousands of dollars). I II III 49.3 55.7 38.7 43.3 25.0 37.3 32.6 41.5 10.9 27.1 29.4 32.9 38.5 39.9 15.5 36.5 42.2 20.4 Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of the three types of companies? Use...
A random sample of companies in electric utilities (I), financial services (II), and food processing (III)...
A random sample of companies in electric utilities (I), financial services (II), and food processing (III) gave the following information regarding annual profits per employee (units in thousands of dollars). I II III 49.3 55.7 38.7 43.3 25.0 37.3 32.6 41.5 10.9 27.1 29.4 32.9 38.5 39.9 15.5 36.5 42.2 20.4 Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of the three types of companies? Use...
A random sample of companies in electric utilities (I), financial services (II), and food processing (III)...
A random sample of companies in electric utilities (I), financial services (II), and food processing (III) gave the following information regarding annual profits per employee (units in thousands of dollars). I II III 49.7 55.8 38.9 43.3 25.3 37.7 32.9 41.7 10.7 27.4 29.2 32.6 38.3 39.6 15.2 36.8 42.5 20.1 Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of the three types of companies? Use...
Another type of painted ceramic vessel is called three-circle red-on-white ( Mimbres Mogollon Archaeology). At four...
Another type of painted ceramic vessel is called three-circle red-on-white ( Mimbres Mogollon Archaeology). At four different sites in an archaeological region, the number of such sherds was counted in local dwelling excavations. Site I Site II Site III Site IV 18 11 37 17 28 4 19 23 9 35 11 17 22 3 45 36 10 29 19 11 11 Shall we reject or not reject the claim that there is no difference in the population mean three-circle...
Where are the deer? Random samples of square-kilometer plots were taken in different ecological locations of...
Where are the deer? Random samples of square-kilometer plots were taken in different ecological locations of a national park. The deer counts per square kilometer were recorded and are shown in the following table. Mountain Brush Sagebrush Grassland Pinon Juniper 34 15 1 31 58 7 24 15 10 25 26 13 Shall we reject or accept the claim that there is no difference in the mean number of deer per square kilometer in these different ecological locations? Use a...
There is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of...
There is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is called Mimbres classic black-on-white. At three different sites, the number of such sherds was counted in local dwelling excavations. Site I Site II Site III 62 29 17 39 18 34 27 54 74 17 60 28 81 18 52 12 23 Shall we reject or not reject the claim that there...
There is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of...
There is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is called Mimbres classic black-on-white. At three different sites, the number of such sherds was counted in local dwelling excavations. Site I Site II Site III 64 26 15 35 17 32 22 54 65 11 68 28 77 16 54 13 20 Shall we reject or not reject the claim that there...
There is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of...
There is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is called Mimbres classic black-on-white. At three different sites, the number of such sherds was counted in local dwelling excavations. Site I Site II Site III 65 20 10 30 15 33 23 57 71 15 60 23 77 13 50 18 29 Shall we reject or not reject the claim that there...
How productive are U.S. workers? One way to answer this question is to study annual profits...
How productive are U.S. workers? One way to answer this question is to study annual profits per employee. A random sample of companies in computers (I), aerospace (II), heavy equipment (III), and broadcasting (IV) gave the following data regarding annual profits per employee (units in thousands of dollars). I II III IV 27.5 13.8 22.1 17.6 23.1 9.5 20.3 16.8 14.3 11.3 7.7 14.3 8.9 8.3 12.5 15.1 11.1 6.1 7.9 10.6 19.5 9.8 Shall we reject or not reject...