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TUT 2 on ANOVA and Ch.18 linked to Ch 13 Preparation
Question 1
In order to measure the intensity of sound, random samples were drawn from the
following populations (numbered in the table below) and the sound made measured in
decibels (dB):
Sample size Average Standard deviation
1 = Normal conversation 10 60 4.5
2 = A car engine 10 70 4.8
3 = An Mp3 player at maximum volume 15 105 5.5
4 = Sound of a washing machine 8 60 4.8
5 = Sound of a lawnmower 5 105 5.8
An analysis of variance (ANOVA) is conducted to determine whether differences exist
between the mean (average) sound intensity for the different sources of sound. Assume
that the necessary conditions for an analysis of variance are being met.
a) The response variable is:
b) The factor of this investigation is:
c) The number of levels of the factor is:
d) The number of responses is:
e) The overall mean intensity of sound, 𝑥𝑥̿ is:
f) Complete the following ANOVA (to 2 decimals, if necessary) table under the
assumption that all the necessary requirements are met.
Source of Variation 𝑆𝑆𝑆𝑆 df MS F p-value
Between groups
0.0000
Within groups
1108.95
Total
21775.62
g) The alternative hypothesis will be:
A. All the population variances are the same.
B. Not all the population variances are the same.
C. At least two of the population variances differ.
D. All the population means are equal.
E. Not all population means are equal.
h) At a 5% level of significance, the decision is:
A. Do not reject 𝐻𝐻0
B. Reject 𝐻𝐻0
i) Conclusion:
TUT 2 on ANOVA and Ch.18 linked to Ch 13 Preparation
Question 1
In order to measure the intensity of sound, random samples were drawn from the
following populations (numbered in the table below) and the sound made measured in
decibels (dB):
Sample size Average Standard deviation
1 = Normal conversation 10 60 4.5
2 = A car engine 10 70 4.8
3 = An Mp3 player at maximum volume 15 105 5.5
4 = Sound of a washing machine 8 60 4.8
5 = Sound of a lawnmower 5 105 5.8
An analysis of variance (ANOVA) is conducted to determine whether differences exist
between the mean (average) sound intensity for the different sources of sound. Assume
that the necessary conditions for an analysis of variance are being met.
a) The response variable is:
b) The factor of this investigation is:
c) The number of levels of the factor is:
d) The number of responses is:
e) The overall mean intensity of sound, 𝑥𝑥̿ is:
f) Complete the following ANOVA (to 2 decimals, if necessary) table under the
assumption that all the necessary requirements are met.
Source of Variation 𝑆𝑆𝑆𝑆 df MS F p-value
Between groups
0.0000
Within groups
1108.95
Total
21775.62
g) The alternative hypothesis will be:
A. All the population variances are the same.
B. Not all the population variances are the same.
C. At least two of the population variances differ.
D. All the population means are equal.
E. Not all population means are equal.
h) At a 5% level of significance, the decision is:
A. Do not reject 𝐻𝐻0
B. Reject 𝐻𝐻0
i) Conclusion:
