Respuesta :
Answer:
CI 95%(μ)= [13.506 ; 14.094]
Step-by-step explanation:
The confidence interval (CI) formula is:
CI (1-alpha) (μ)= mean+- [(Z(alpha/2))* σ/sqrt(n)]
alpha= is the proportion of the distribution tails that are outside the confidence interval. In this case, 5% because 100-90%
Z(5%/2)= is the critical value of the standardized normal distribution. In this case is 1.96
σ= standard deviation. In this case 0.75 day
mean= 13.8 days
n= number of observations . In this case 25
Then, the confidence interval (90%) is:
CI 95%(μ)= 13.8+- [1.96*(0.75/sqrt(25)]
CI 95%(μ)= 13.8+- [1.96*(0.75/5) ]
CI 95%(μ)= 13.8+- (0.294)
CI 95%(μ)= [13.8-0.294 ; 13.8+0.294]
CI 95%(μ)= [13.506 ; 14.094]
The 95% confidence interval for μ based on the given data is; CI = (13.506, 14.094)
What is the confidence interval?
We are given;
Sample mean; x' = 13.8 days
Standard deviation; σ = 0.75 days
Sample size; n = 25
confidence level = 95%
z-score at 95% confidence level is 1.96
Formula for confidence level is;
CI = x' ± z(σ/√n)
CI = 13.8 ± 1.96(0.75/√25)
CI = 13.8 ± 0.294
CI = (13.8 - 0.294), (13.8 + 0.294)
CI = (13.506, 14.094)
Read more about confidence interval at; https://brainly.com/question/17097944
