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Alenkasestr [34]
3 years ago
12

An environmentalist wants to find out the fraction of oil tankers that have spills each month. Step 2 of 2 : Suppose a sample of

333 tankers is drawn. Of these ships, 257 did not have spills. Using the data, construct the 80% confidence interval for the population proportion of oil tankers that have spills each month. Round your answers to three decimal places.
Mathematics
1 answer:
rewona [7]3 years ago
6 0

Answer:

The 80% confidence interval for the population proportion of oil tankers that have spills each month is (0.199, 0.257).

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}.

Suppose a sample of 333 tankers is drawn. Of these ships, 257 did not have spills.

333 - 257 = 76 have spills.

This means that n = 333, \pi = \frac{76}{333} = 0.228

80% confidence level

So \alpha = 0.2, z is the value of Z that has a pvalue of 1 - \frac{0.2}{2} = 0.9, so Z = 1.28.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.228 - 1.28\sqrt{\frac{0.228*0.772}{333}} = 0.199

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.228 + 1.28\sqrt{\frac{0.228*0.772}{333}} = 0.257

The 80% confidence interval for the population proportion of oil tankers that have spills each month is (0.199, 0.257).

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Given:

sequences: -1,4,-7,10,...

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Solution:

A sequence forms an arithmetic progression if difference between terms remain same.

A sequence forms a geometric progression if ratio of the consecutive terms is same.

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So, -1,4,-7,10,... is neither an arithmetic progression nor a geometric progression.

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As ratio of the consecutive terms is same, the sequence forms a geometric progression.

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As the difference between the consecutive terms is the same, the sequence forms an arithmetic progression.

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