An article included data from a survey of a random sample of adults living in the United States. Of the
1,400 people who participated in the survey, 700 responded they believe that global climate change is a
major threat to the well-being of the United States.
Use the five-step process for estimation problems (EMC^3 ) to construct a 95% confidence interval for the
proportion of adults in the United States who believe that global climate change is a major threat to the
well-being of the United States.
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Step 1: Identify the parameter of interest
The parameter of interest in this case is the proportion of adults in the United States who believe that global climate change is a major threat to the well-being of the United States.
Step 2: State the hypotheses
Since we are constructing a confidence interval, we do not need to state any hypotheses.
Step 3: Select the appropriate confidence level
The confidence level for this problem is given as 95%.
Step 4: Find the critical value(s)
To find the critical value(s), we need to use the z-table for a 95% confidence level. The critical value for a 95% confidence level is approximately 1.96.
Step 5: Calculate the confidence interval
The formula to calculate the confidence interval is:
CI = p̂ ± z * √(p̂(1-p̂)/n)
Where:
CI = Confidence interval
p̂ = Sample proportion
z = Critical value
n = Sample size
In this case, p̂ = 700/1400 = 0.5 (since half of the respondents said they believe global climate change is a major threat), z = 1.96 (from step 4), and n = 1400.
CI = 0.5 ± 1.96 * √(0.5(1-0.5)/1400)
CI = 0.5 ± 0.0259
CI = (0.4741, 0.5259)
Therefore, the 95% confidence interval for the proportion of adults in the United States who believe that global climate change is a major threat to the well-being of the United States is (0.4741, 0.5259).
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