Question 5 A study was conducted to compare the pollution levels of two lakes (Lake A and Lake B). The pollution levels are compared by using the dissolved oxygen levels in the water. Lower dissolved oxygen levels are indicative of higher pollution levels. Seven water specimens from Lake A and six water specimens from Lake B are randomly and independently selected, and the dissolved oxygen levels (measured in mg/L) of the water specimens are recorded as follows. Lake A Lake B 7.2 6.8 7.1 6.3 7.5 6.5 6.9 6.3 5.7 6.5 6.1 5.8 5.3 2 Assume that the dissolved oxygen levels of water from both lakes are normally distributed. (a) At the 0.01 level of significance, is there sufficient evidence to conclude that Lake B is more polluted than Lake A? (b) At the 0.05 level of significance, do the data provide sufficient evidence to conclude that the population standard deviation of the dissolved oxygen level of water in Lake B is different from 0.4? (c) At the 0.05 level of significance, do the data provide sufficient evidence to conclude that the population standard deviation of the dissolved oxygen level of water in Lake B is higher than that in Lake A?

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Question 5
A study was conducted to compare the pollution levels of two lakes (Lake A and Lake B).
The pollution levels are compared by using the dissolved oxygen levels in the water. Lower
dissolved oxygen levels are indicative of higher pollution levels. Seven water specimens
from Lake A and six water specimens from Lake B are randomly and independently selected,
and the dissolved oxygen levels (measured in mg/L) of the water specimens are recorded as
follows.
Lake A
Lake B
7.2
6.8
7.1
6.3
7.5
6.5
6.9
6.3
5.7
6.5
6.1
5.8
5.3
2
Assume that the dissolved oxygen levels of water from both lakes are normally distributed.
(a) At the 0.01 level of significance, is there sufficient evidence to conclude that Lake B is
more polluted than Lake A?
(b) At the 0.05 level of significance, do the data provide sufficient evidence to conclude
that the population standard deviation of the dissolved oxygen level of water in Lake B
is different from 0.4?
(c) At the 0.05 level of significance, do the data provide sufficient evidence to conclude
that the population standard deviation of the dissolved oxygen level of water in Lake B
is higher than that in Lake A?
Transcribed Image Text:Question 5 A study was conducted to compare the pollution levels of two lakes (Lake A and Lake B). The pollution levels are compared by using the dissolved oxygen levels in the water. Lower dissolved oxygen levels are indicative of higher pollution levels. Seven water specimens from Lake A and six water specimens from Lake B are randomly and independently selected, and the dissolved oxygen levels (measured in mg/L) of the water specimens are recorded as follows. Lake A Lake B 7.2 6.8 7.1 6.3 7.5 6.5 6.9 6.3 5.7 6.5 6.1 5.8 5.3 2 Assume that the dissolved oxygen levels of water from both lakes are normally distributed. (a) At the 0.01 level of significance, is there sufficient evidence to conclude that Lake B is more polluted than Lake A? (b) At the 0.05 level of significance, do the data provide sufficient evidence to conclude that the population standard deviation of the dissolved oxygen level of water in Lake B is different from 0.4? (c) At the 0.05 level of significance, do the data provide sufficient evidence to conclude that the population standard deviation of the dissolved oxygen level of water in Lake B is higher than that in Lake A?
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