A report summarized a survey of 2,315 working adults. The report indicates that 463 of the working adults surveyed said they were very concerned that their job will be automated, outsourced, or otherwise made obsolete in the next 5 years. The sample was selected in a way designed to produce a representative sample of working adults. Construct and interpret a 95% confidence interval for the proportion of working adults who are very concerned that their job will be automated, outsourced, or otherwise made obsolete in the next 5 years. Step 1 A confidence interval for a population proportion p can be constructed if the following criteria have been met. 1. The sample size n is large enough so that no 210 and n(1 - p) ≥ 10. 2. If the sample is selected without replacement, the sample size is small relative to the population size. That is, n is at most 10% of the population size. 3. The sample proportion p is from a simple random sample. To determine if the criteria are met for constructing a confidence interval for the population proportion of workers who are concerned their job will become obsolete in the next 5 years, we must first calculate the sample proportion. There were 2,315 working adults surveyed, giving n = 2,315. It is given that 463 of those surveyed are concerned that their job will become obsolete in the next 5 years. Use these values to calculate the sample proportion of workers who are concerned their job will become obsolete in the next 5 years. number of successes in a sample n 463 2,315 0.2 Substituting the values of n and p, we get nø Thus, the first condition has been met. The sample was drawn from the population of all working adults. It is the population of all working adults. Thus, the second condition has x and n(1-p) = [ ✔ reasonable to assume that 2,315 is less than 10% of been met. We are told the sample was selected in a way to produce a representative sample of working adults. Thus, the third condition [has been met.

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A report summarized a survey of 2,315 working adults. The report indicates that 463 of the working adults surveyed said they were very
concerned that their job will be automated, outsourced, or otherwise made obsolete in the next 5 years. The sample was selected in a way
designed to produce a representative sample of working adults. Construct and interpret a 95% confidence interval for the proportion of
working adults who are very concerned that their job will be automated, outsourced, or otherwise made obsolete in the next 5 years.
Step 1
A confidence interval for a population proportion p can be constructed if the following criteria have been met.
To determine if the criteria are met for constructing a confidence interval for the population proportion of workers who are concerned their job
will become obsolete in the next 5 years, we must first calculate the sample proportion. There were 2,315 working adults surveyed, giving
n = 2,315.
It is given that 463 of those surveyed are concerned that their job will become obsolete in the next 5 years. Use these values to calculate the
sample proportion of workers who are concerned their job will become obsolete in the next 5 years.
number of successes in a sample
n
p
1. The sample size n is large enough so that no 2 10 and n(1 - p) ≥ 10.
2. If the sample is selected without replacement, the sample size is small relative to the population size. That is, n is at most
10% of the population size.
3. The sample proportion is from a simple random sample.
463
= 0.2
2,315
Substituting the values of n and p, we get no =
Thus, the first condition has
The sample was drawn from the population of all working adults. It is
the population of all working adults. Thus, the second condition has
X and n(1-p) =
been met.
reasonable to assume that 2,315 is less than 10% of
been met.
We are told the sample was selected in a way to produce a representative sample of working adults. Thus, the third condition has
been met.
Transcribed Image Text:A report summarized a survey of 2,315 working adults. The report indicates that 463 of the working adults surveyed said they were very concerned that their job will be automated, outsourced, or otherwise made obsolete in the next 5 years. The sample was selected in a way designed to produce a representative sample of working adults. Construct and interpret a 95% confidence interval for the proportion of working adults who are very concerned that their job will be automated, outsourced, or otherwise made obsolete in the next 5 years. Step 1 A confidence interval for a population proportion p can be constructed if the following criteria have been met. To determine if the criteria are met for constructing a confidence interval for the population proportion of workers who are concerned their job will become obsolete in the next 5 years, we must first calculate the sample proportion. There were 2,315 working adults surveyed, giving n = 2,315. It is given that 463 of those surveyed are concerned that their job will become obsolete in the next 5 years. Use these values to calculate the sample proportion of workers who are concerned their job will become obsolete in the next 5 years. number of successes in a sample n p 1. The sample size n is large enough so that no 2 10 and n(1 - p) ≥ 10. 2. If the sample is selected without replacement, the sample size is small relative to the population size. That is, n is at most 10% of the population size. 3. The sample proportion is from a simple random sample. 463 = 0.2 2,315 Substituting the values of n and p, we get no = Thus, the first condition has The sample was drawn from the population of all working adults. It is the population of all working adults. Thus, the second condition has X and n(1-p) = been met. reasonable to assume that 2,315 is less than 10% of been met. We are told the sample was selected in a way to produce a representative sample of working adults. Thus, the third condition has been met.
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