Final answer:
To estimate the proportion of adults who believe human cloning should not be allowed with 98% confidence, calculate the sample proportion, find the z-score for the desired confidence level, compute the margin of error, and determine the confidence interval by adding and subtracting the margin of error from the sample proportion.
Step-by-step explanation:
To construct a 98% confidence interval estimate of the proportion of adults believing that cloning of humans should not be allowed, we can use the formula for the confidence interval of a proportion, which is given by:
p ± z * √(p(1 - p) / n), where:
- p is the sample proportion
- z is the z-score corresponding to the desired confidence level
- n is the sample size
In this case, the sample proportion (p) is 901/1012, which is the number of adults who said cloning should not be allowed divided by the total number surveyed. The z-score for a 98% confidence level is approximately 2.33 (found in z-score tables or using statistical software). The sample size (n) is 1012.
Substituting these values into the formula, we calculate our confidence interval.
- Calculate the sample proportion: p = 901/1012
- Find the z-score for a 98% confidence level: z = 2.33
- Calculate the standard error: SE = √(p(1 - p) / n)
- Multiply the standard error by the z-score: Margin of Error (MOE) = z * SE
- Add and subtract the MOE from the sample proportion to find the interval: p ± MOE
After performing these calculations, we have a 98% confidence interval that provides an estimate of the true proportion of adults who believe cloning should not be allowed.