An article about the relative priorities of protecting the environment and the economy in America
summarized a survey of 1,600 adult U.S. citizens. When asked whether protecting the environment or
protecting jobs should have a higher priority, 848 of the survey participants chose protecting the
environment. The article states that participants were selected to be representative of all adult U.S.
citizens.
(a) Estimate the proportion of adult U.S. citizens who think that protecting the environment should be a
higher priority than protecting jobs. What statistic did you use?
(b) Use the sample data to estimate the standard error of p̂
(c) Calculate the margin of error associated with the estimate in Part (a). (Round your answer to three
decimal places.)
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(a) 0.53
sample proportion
(b) 0.0125
(c) 0.024
It is unlikely that the estimated proportion of adult U.S. citizens who think that protecting the
environment should be a higher priority than protecting jobs differs from the true population
proportion by more than the calculated value.
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(a) To estimate the proportion of adult U.S. citizens who think that protecting the environment should be a higher priority than protecting jobs, we use the statistic of the sample proportion.
The proportion of adults who chose protecting the environment is calculated as:
p̂ = (# of participants who chose protecting the environment / Total number of participants)
= 848 / 1600
≈ 0.530
Therefore, the estimated proportion of adult U.S. citizens who think that protecting the environment should be a higher priority than protecting jobs is approximately 0.530.
(b) To estimate the standard error of p̂, we use the formula:
SE(p̂) = √[(p̂(1 - p̂)) / n], where n is the sample size.
Substituting the given values:
SE(p̂) = √[(0.53(1 - 0.53)) / 1600]
= √[0.53(0.47) / 1600]
≈ √[0.0251 / 1600]
≈ √0.0000157
≈ 0.00396
Therefore, the estimated standard error of p̂ is approximately 0.00396.
(c) The margin of error associated with the estimate in Part (a) can be calculated as:
ME = z * SE(p̂), where z is the critical value for the desired level of confidence.
Assuming a 95% confidence level (which corresponds to a z-value of 1.96 for a large sample size):
ME = 1.96 * 0.00396
≈ 0.00775
Rounding to three decimal places, the margin of error associated with the estimate in Part (a) is approximately 0.008.
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