Answer
↓Steps Explained:↓
Construct a 95% confidence interval for the proportion value p
from a population of 100 and a sample size of 40
Confidence Interval Formula for p formula
p^ - zscoreα * σp/√p < p < p^ + zscoreα * σp/√p where:
X = sample mean, s = sample standard deviation, zscore = Normal distribution Z-score from a probability where α = (1 - Confidence Percentage)/2
Calculate p^:
Calculate σp
| σp = | √p^(1 - p^) |
| √N |
| σp = | √0.4(1 - 0.4) |
| √100 |
| σp = | √0.4(0.6) |
| √100 |
| σp = | √0.24 |
| √100 |
σp
σp = 0.048989794855664
Calculate α
α = 1 - Confidence%
α = 1 - 0.95
α = 0.05
Find α spread range:
α = ½(α)
α = ½(0.05)
α = 0.025
Find z-score for α value for 0.025
zscore0.025 = 1.96 <--- Value can be found on Excel using =NORMSINV(0.975)
Calculate Margin of Error:
MOE = σp x z-score
MOE = 0.048989794855664 x 1.96
MOE = 0.096019997917101
Calculate high end confidence interval total:
High End = p^+ zscoreα x σp
High End = 0.4 + 1.96 * 0.048989794855664
High End = 0.4 + 0.096019997917101
High End = 0.496
Calculate low end confidence interval total:
Low End = p^ - zscoreα x σp
Low End = 0.4 - 1.96 * 0.048989794855664
Low End = 0.4 - 0.096019997917101
Low End = 0.304
Final Answer
0.304 < p < 0.496Take the Quiz Switch to Chat Mode
Related Calculators: Proportion Sample Size | Difference of Proportions Test | Confidence Interval/Hypothesis Testing for the Difference of Means
What this means is if we repeated experiments, the proportion of such intervals that contain p would be 95%