Question

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 the four types of companies? Use a 5% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

Ho: μ1 = μ2 = μ3 = μ4; H1: Not all the means are equal.

Ho: μ1 = μ2 = μ3 = μ4; H1: All four means are different.

Ho: μ1 = μ2 = μ3 = μ4; H1: Exactly two means are equal.

Ho: μ1 = μ2 = μ3 = μ4; H1: Exactly three 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.

P-value > 0.100

0.050 < P-value < 0.100

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.001 < P-value < 0.010

P-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 = 0.05, we do not reject H0.

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

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

Since the P-value is less than or equal to the level of significance at α = 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 Within groups Total

Answer #1

# part -f

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...

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
27.3
13.6
22.9
17.2
23.8
9.1
20.6
16.1
14.1
11.3
7.3
14.3
8.9
8.6
12.4
15.5
11.9
6.6
7.6
10.5
19.7
9.9
Shall we reject or not reject...

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 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 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...

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. 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...

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...

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) 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...

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