Question

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 1% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

*H _{o}*:

(b) Find *SS _{TOT}, SS_{BET}*, and

SS_{TOT} |
= | |

SS_{BET} |
= | |

SS_{W} |
= |

Find *d.f. _{BET}, d.f._{W},
MS_{BET}*, and

df_{BET} |
= | |

df_{W} |
= | |

MS_{BET} |
= | |

MS_{W} |
= |

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 > 0.1000.050 < *P*-value <
0.100 0.025 < *P*-value <
0.0500.010 < *P*-value < 0.0250.001 <
*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* = 0.01, we do not reject
*H*_{0}.Since the *P*-value is less than or
equal to the level of significance at *α* = 0.01, we reject
*H*_{0}. Since the
*P*-value is greater than the level of significance at
*α* = 0.01, we reject *H*_{0}.Since the
*P*-value is less than or equal to the level of significance
at *α* = 0.01, we do not reject *H*_{0}.

(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.

Source of Variation |
Sum of Squares |
Degrees of Freedom |
MS |
FRatio |
P Value |
Test Decision |

Between groups | ---Select--- 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 | ---Select--- Do not reject H0. Reject H0. | ||||

Within groups | ||||||

Total |

Answer #1

d)

Since the P-value is less than or equal to the level of significance at alpha= 0.01, we reject H0.

e)

At the 1% level of significance there is sufficient evidence to conclude that the means are all equal.

f)

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...

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) 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...

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
55.3
38.7
43.7
24.7
37.7
32.6
41.3
10.7
27.5
29.8
32.8
38.1
39.1
15.5
36.7
42.1
20.8
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 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...

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...

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...

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...

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
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