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kolezko [41]
3 years ago
12

The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 44

who smoke. Step 2 of 2 : Suppose a sample of 632 Americans over 44 is drawn. Of these people, 462 don't smoke. Using the data, construct the 90% confidence interval for the population proportion of Americans over 44 who smoke. Round your answers to three decimal places.
Mathematics
1 answer:
xenn [34]3 years ago
4 0

Answer:

The 90% confidence interval for the population proportion of Americans over 44 who smoke is (0.24, 0.298)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

632 American, 462 don't smoke, 632 - 462 = 170 smoke.

Proportion who smoke, so

n = 632, \pi = \frac{170}{632} = 0.269

90% confidence level

So \alpha = 0.1, z is the value of Z that has a pvalue of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.269 - 1.645\sqrt{\frac{0.269*0.731}{632}} = 0.24

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.269 + 1.645\sqrt{\frac{0.269*0.731}{632}} = 0.298

The 90% confidence interval for the population proportion of Americans over 44 who smoke is (0.24, 0.298)

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Answer:

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Step-by-step explanation:

1. Let's see what happens in the conference room the first 20 minutes, according to the graph:

The temperature increase from 65 °F to 75 °F. This fact discards immediately answer B, that mentions that "the temperature of the room decreases steadily to a comfortable temperature".

2. Let's see what happens in the conference room the next 20 minutes (between minutes 20 and 40), according to the graph:

The temperature remains at 75 °F, at a comfortable temperature, during these 20 minutes. This fact discards answer D because it mentions that the "room becomes too hot", which is not true because the additional 10 °F of increase is most likely, not "too much" and it also considers 65 °F as "too cold".

3. Let's see what happens in the conference room between minutes 40 and 50, according to the graph:

In ten minutes, the temperature decreases from 75 °F to 65 °F, which was the original temperature of the room. No big difference between answers A and C, the only that are still valid.

4. Let's see what happens in the conference room between minutes 50 and 80, according to the graph:

In these 30 minutes, the temperature of the conference room again increases between minutes 50 and 70 from 65 °F to 75 °F. This last fact discards the answer A, that mentions that " finally, Aaron turns the heat back on and the temperature of the room increases steadily for the rest of the conference". What actually happened is that the temperature becomes comfortable again and stays the same the rest of the conference.

<u>This is a detailed explanation why we discard answers A, C and D and we select answer C as the right one.</u>

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Answer:

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Step-by-step explanation:

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simplifying to:

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factoring to:

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if x=5 then y=2(5)-3=7

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