According to a Gallup Poll conducted in March of 2009, 38% of American adults polled believe that global warming will pose a serious threat to them or their way of life in their lifetime. Assuming a sample size of 1000, calculate a 95% confidence interval for estimating the population proportion of all American adults who believe that global warming will pose a serious threat to them or their way of life in their lifetime.

Question

According to a Gallup Poll conducted in March of 2009, 38% of American adults polled believe that global warming will pose a serious threat to them or their way of life in their lifetime. Assuming a sample size of 1000, calculate a 95% confidence interval for estimating the population proportion of all American adults who believe that global warming will pose a serious threat to them or their way of life in their lifetime.

Answer 1

To calculate the 95% confidence interval for estimating a population proportion, you can use the formula:

CI = p̂ ± z * √(p̂(1-p̂)/n)

where:
CI is the confidence interval
p̂ is the sample proportion
z is the z-score corresponding to the desired level of confidence (for 95% confidence, z = 1.96)
n is the sample size

In this case, the sample proportion (p̂) is given as 38% or 0.38, and the sample size (n) is 1000.

Now let's substitute these values into the formula:

CI = 0.38 ± 1.96 * √(0.38(1-0.38)/1000)

Calculating the square root and performing the multiplication gives:

CI = 0.38 ± 1.96 * √(0.38 * 0.62)/1000)

CI = 0.38 ± 1.96 * √(0.2356)/1000

CI = 0.38 ± 1.96 * 0.1534/1000

CI = 0.38 ± 0.3009/1000

CI = 0.38 ± 0.00087

So, the 95% confidence interval for estimating the population proportion of American adults who believe that global warming will pose a serious threat to them or their way of life in their lifetime is approximately 0.3791 to 0.3809.