Question

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 the Wind Mountain archaeological region, the number of such sherds was counted in local dwelling excavations.

Site I Site II Site III Site IV
14 17 39 10
29 3 17 22
4 35 12 15
20 6 49 31
11 24 13
18 17

Shall we reject or not reject the claim that there is no difference in the population mean three-circle red-on-white sherd counts for the four sites? Use a 5% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

Ho: ?1 = ?2 = ?3 = ?4; H1: Exactly three means are equal.

Ho: ?1 = ?2 = ?3 = ?4; H1: All four means are different.    

Ho: ?1 = ?2 = ?3 = ?4; H1: Not all the means are equal.

Ho: ?1 = ?2 = ?3 = ?4; H1: Exactly two means are equal.



(b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.)

SSTOT =
SSBET =
SSW =


Find d.f.BET, d.f.W, MSBET, and MSW. (Use 3 decimal places for MSBET, and MSW.)

dfBET =
dfW =
MSBET =
MSW =


Find the value of the sample F statistic. (Use 3 decimal places.)


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

(c) Find the P-value of the sample test statistic. (Use 4 decimal places.)

(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 ? = 0.05, we do not reject H0.

Since the P value is less than or equal to the level of significance at ? = 0.05, we reject H0.   

Since the P value is greater than the level of significance at ? = 0.05, we reject H0.

Since the P value is less than or equal to the level of significance at ? = 0.05, we do not reject H0.


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

At the 5% level of significance there is insufficient evidence to conclude that the means are not all equal.

At the 5% level of significance there is sufficient evidence to conclude that the means are all equal.  

  At the 5% level of significance there is insufficient evidence to conclude that the means are all equal.

At the 5% 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.

Source of
Variation.
Sum of.   
Squares
Degrees of
Freedom
MS.    F
Ratio
P Value. Test
Decision
Between groups Do not reject H0/Reject H0.
Within groups
Total

Homework Answers

Answer #1

a) The null and alternate hypotheses are

against H1 : Not all the means are equal.

b) SSTOT = 2766.7, SSBET = 2264.8, SSW = 501.9

dfBET = 3, dfW = 17

MSBET = 167.3, MSW = 133.2

The value of the sample F statistic = 1.26

The degrees of freedom = (3, 17)

c) The P-value of the sample test statistic = 0.321

d) Since the P value is greater than the level of significance at = 0.05, we do not reject H0.

e) At the 5% level of significance there is insufficient evidence to conclude that the means are not all equal.

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
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 15 12 33 11 29 5 23 19 7 33 14 10 22 2 47 38 16 27 15 13 16 Shall we reject or not reject the claim that there is no difference in the population mean three-circle...
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...
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 19 15 38 13 22 8 15 17 5 30 10 16 22 8 47 37 10 24 19 12 18 Shall we reject or not reject the claim that there is no difference in the population mean three-circle...
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 19 12 38 15 27 5 20 17 7 35 16 12 19 3 44 35 17 22 15 17 13 Shall we reject or not reject the claim that there is no difference in the population mean three-circle...
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 49.4 55.8 38.8 43.2 24.7 37.4 32.1 41.4 10.7 27.2 29.6 32.5 38.3 39.7 15.7 36.3 42.1 20.6 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 49.8 55.6 39.1 43.2 25.0 37.7 32.2 41.4 10.5 27.1 29.5 32.1 38.6 39.5 15.6 36.3 42.4 20.2 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...
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 29 24 10 27 59 3 25 16 2 27 24 6 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...
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 (27.6;23.1;14.7;8.9;11.9) II (13.1;9.9;11.7;8.1;6.9;19.5) III ( 22.4;20.2;7.4;12.9;7.7) IV (17.6;16.8;14.4;15.7;10.7;9.4) Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of...
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...
The quantity of dissolved oxygen is a measure of water pollution in lakes, rivers, and streams....
The quantity of dissolved oxygen is a measure of water pollution in lakes, rivers, and streams. Water samples were taken at four different locations in a river in an effort to determine if water pollution varied from location to location. Location I was 500 meters above an industrial plant water discharge point and near the shore. Location II was 200 meters above the discharge point and in midstream. Location III was 50 meters downstream from the discharge point and near...