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 |
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 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 (from the following).

*H _{o}*: μ

*H _{o}*: μ

*H _{o}*: μ

*H _{o}*: μ

(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.

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

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

(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 from the following--- 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 from the following--- Do not reject H0. -- Reject H0. | ||||

Within groups | ||||||

Total |

Answer #1

a)

level of significance =0.05

*H _{o}*: μ

b)

SSTOT | 708.395 |

SSBET | 89.306 |

SSW | 619.089 |

dfBET | 3 |

dfW | 18 |

MSBET | 29.769 |

MSW | 34.394 |

value of test statistic for factor A = | 0.87 |

df(numerator) = | 3 | |

df(Denominator) = | 18 |

c)

p value =0.4770

d) r fail to reject the null hypothesis

e)can not conclude that population means are not equal

f)

Source | SS | df | MS | F | P value |

Between | 89.306 | 3 | 29.769 | 0.866 | 0.4770 |

Within | 619.089 | 18 | 34.394 | ||

Total | 708.395 | 21 |

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...

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
13.7
22.5
17.8
23.6
9.4
20.1
16.4
14.9
11.6
7.7
14.2
8.9
8.6
12.4
15.6
11.8
6.6
7.2
10.7
19.2
9.6
Shall we reject or not reject...

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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
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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
13.5
22.2
17.5
23.8
9.8
20.3
16.9
14.9
11.9
7.9
14.7
8.4
8.8
12.4
15.3
11.4
6.1
7.4
10.5
19.8
9.2
Shall we reject or not reject...

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...

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...

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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