Question

Six samples of each of four types of cereal grain grown in a certain region were analyzed to determine thiamin content, resulting in the following data (µg/g). Wheat 5.1 4.6 6.0 6.0 6.7 5.7 Barley 6.5 8.0 6.1 7.5 5.8 5.5 Maize 5.7 4.6 6.4 4.9 6.0 5.3 Oats 8.2 6.0 7.9 7.1 5.4 7.1 Does this data suggest that at least two of the grains differ with respect to true average thiamin content? Use a level α = 0.05 test. State the appropriate hypotheses. H0: μ1 = μ2 = μ3 = μ4 Ha: at least two μi's are unequal H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4 Ha: at least two μi's are equal H0: μ1 = μ2 = μ3 = μ4 Ha: all four μi's are unequal H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4 Ha: all four μi's are equal Compute the test statistic value. (Round your answer to two decimal places.) f = What can be said about the P-value for the test? P-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 P-value < 0.001 State the conclusion in the problem context. Fail to reject H0. There is not significant evidence that at least two of the grains differ in average thiamin content. Reject H0. There is significant evidence that at least two of the grains differ in average thiamin content. Fail to reject H0. There is significant evidence that at least two of the grains differ in average thiamin content. Reject H0. There is not significant evidence that at least two of the grains differ in average thiamin content.

Answer #1

We can directly use here one way anova by Excel.

Step1) Enter data in Excel.

Step 2) Data >>Data analysis >> One way anova >>Select data >>click on label in first row >>ok

Null and alternative hypothesis

H0: μ1 = μ2 = μ3 = μ4 vs Ha: at least two μi's are unequal

test statistic F value is =3.74

P value is 0.028

0.010 < P-value < 0.050

Reject H0. There is significant evidence that at least two of the grains differ in average thiamin content.

The following data was reported on total Fe for four types of
iron formation (1 = carbonate, 2 = silicate, 3 = magnetite, 4 =
hematite).
1:
21.0
28.1
27.8
27.0
27.5
25.2
25.3
27.1
20.5
31.3
2:
26.7
24.0
26.2
20.2
23.8
34.0
17.1
26.8
23.7
24.6
3:
30.1
34.0
27.5
29.4
28.0
26.2
29.9
29.5
30.0
35.6
4:
36.3
44.2
34.1
30.3
32.1
33.1
34.1
32.9
36.3
25.7
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respectively.) 1.6: 59.7 53.3 56.1 63.3 58.9 3.8: 55.1 59.7 52.8
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6: 420.1 347.2 361.0 404.5 331.0 348.9 381.7
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The following data were obtained for a randomized block design
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places.)
Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F
p-value
Treatments
Blocks
Error
Total
Test for any significant differences. Use α = 0.05.
State the null and alternative hypotheses.
H0: Not...

An experiment has been conducted for four treatments with seven
blocks. Complete the following analysis of variance table. (Round
your values for mean squares and F to two decimal places,
and your p-value to three decimal places.)
Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F
p-value
Treatments
900
Blocks
200
Error
Total
1,600
Use α = 0.05 to test for any significant
differences.
State the null and alternative hypotheses.
H0: At least two of the population...

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 long it takes paint to dry can have an impact on the
production capacity of a business. An auto body & paint
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An interesting question is, "Do all paint-drying robots have the
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You may need to use the appropriate technology to answer this
question.
An experiment has been conducted for four treatments with seven
blocks. Complete the following analysis of variance table. (Round
your values for mean squares and F to two decimal places,
and your p-value to three decimal places.)
Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F
p-value
Treatments
300
Blocks
700
Error
100
Total
1,100
Use α = 0.05 to test for any significant
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Three different methods for assembling a product were proposed
by an industrial engineer. To investigate the number of units
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Where are the deer? Random samples of square-kilometer plots
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34
15
1
31
58
7
24
15
10
25
26
13
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