A pharmaceuitical company found that 46% of 100 U,S adults sampled surveyed know neither their blood pressure nor their chlosterol levels assuming the person surveyed to be a simple random sample of u,s adults construct a 95% confidence interval for population proportion of u,s adults who would have given the same answer if a cenus had been taken instead of survey?
We can use the formula for the confidence interval for a population proportion:
CI = p̂ ± z*√(p̂(1-p̂)/n)
where:
p̂ = sample proportion = 0.46
z = z-score for 95% confidence level = 1.96
n = sample size = 100
Plugging in the values, we get:
CI = 0.46 ± 1.96*√(0.46(1-0.46)/100)
CI = 0.46 ± 0.098
CI = (0.362, 0.558)
Therefore, we can be 95% confident that the proportion of U.S adults who would not know their blood pressure or cholesterol levels if surveyed in a census is between 0.362 and 0.558.
To construct a 95% confidence interval for the population proportion, we can use the formula:
CI = p̂ ± z * sqrt((p̂ * (1 - p̂)) / n)
Where:
CI = Confidence Interval
p̂ = Sample proportion
z = Z-score corresponding to the desired confidence level
n = Sample size
In this case, the sample proportion (p̂) is given as 46% or 0.46, the sample size (n) is 100, and we want a 95% confidence level.
First, we need to find the Z-score corresponding to a 95% confidence level. The Z-score can be found using a standard normal distribution table or calculator. For a 95% confidence level, the Z-score is approximately 1.96.
Calculating the Confidence Interval:
CI = 0.46 ± 1.96 * sqrt((0.46 * (1 - 0.46)) / 100)
Now we can calculate the boundaries of the confidence interval by plugging in the values:
CI = 0.46 ± 1.96 * sqrt((0.46 * 0.54) / 100)
CI = 0.46 ± 1.96 * sqrt(0.2484 / 100)
CI = 0.46 ± 1.96 * 0.04984
CI = 0.46 ± 0.09779
Finally, we can calculate the confidence interval:
Lower Bound = 0.46 - 0.09779 = 0.36221
Upper Bound = 0.46 + 0.09779 = 0.55779
Therefore, the 95% confidence interval for the population proportion of US adults who would give the same answer if a census were taken instead of a survey is approximately 0.36221 to 0.55779.