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Reliance on solid biomass fuel for cooking and heating exposes many children from developing countries to high levels of indoor air pollution. An article presented information on various pulmonary characteristics in samples of children whose households in India used either biomass fuel or liquefied petroleum gas (LPG). For the 756 children in biomass households, the sample mean peak expiratory flow (a person's maximum speed of expiration) was 3.8 L/s, and the sample standard deviation was 1.2. For the 755 children whose households used liquefied petroleum gas, the sample mean PEF was 4.37 and the sample standard deviation was 1.19.
(a) Calculate a confidence interval at the 95% confidence level for the population mean PEF for children in biomass households and then do likewise for children in LPG households. (Round your answers to two decimal places.)

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Answer:

The 95% confidence interval for the population mean PEF for children in biomass households is (1.448L/s, 6.152L/s).

The 95% confidence interval for the population mean PEF for children in LPG households is (2.0376L/s, 6.70246L/s).

Step-by-step explanation:

(a) Calculate a confidence interval at the 95% confidence level for the population mean PEF for children in biomass households and then do likewise for children in LPG households.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now we find M as such:

[tex]M = z*s[/tex]

In which s is the sample standard deviation.

For children in biomass households.

For the 756 children in biomass households, the sample mean peak expiratory flow (a person's maximum speed of expiration) was 3.8 L/s, and the sample standard deviation was 1.2.

This means that [tex]\mu = 3.8, \sigma = 1.2[/tex]

So

[tex]M = z*s = 1.96*1.2 = 2.352[/tex]

The lower end of the interval is the mean subtracted by M. So it is 3.8 - 2.352 = 1.448L/s.

The upper end of the interval is the mean added to M. So it is 3.8 + 2.352 = 6.152 L/s.

The 95% confidence interval for the population mean PEF for children in biomass households is (1.448L/s, 6.152L/s).

For children in LPG households

For the 755 children whose households used liquefied petroleum gas, the sample mean PEF was 4.37 and the sample standard deviation was 1.19.

This means that [tex]\mu = 4.37, \sigma = 1.19[/tex]

So

[tex]M = z*s = 1.96*1.19 = 2.3324[/tex]

The lower end of the interval is the mean subtracted by M. So it is 4.37 - 2.3324 = 2.0376L/s.

The upper end of the interval is the mean added to M. So it is 4.37 + 2.3324 = 6.70246L/s.

The 95% confidence interval for the population mean PEF for children in LPG households is (2.0376L/s, 6.70246L/s).

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