In: Statistics and Probability
explain the difference between the confident interval and the confident level. Then provide an example to show us how to correctly interpret a confidence interval.
A confidence interval estimates a population parameter from a sample statistic at a certain level of confidence.
confidence interval gives range of values.
Gives information about closeness to unknown population parameters.
confidence interval stated in terms of level of confidence
egg,95% confident,99% confident
it can never be 100%
Ex:
A supermarket wants to estimate the population mean weight of watermelons of a certain type. A sample size n = 45 has sample mean = 20 pounds with sample standard deviation s = 2.2 pounds. Create a confidence interval at 90% confidence for the population mean μ.
Sol:
n=45
df=n-1=45-1=44
alpha=1-0.90=0.10
alpha/2=0.10/2=0.05
sample mean=xbar=20
sample standard deviation=s=2.2
t crit for 0.05 level of significance and 44 df is
=T.INV(0.05;44)
=1.6802
90% confidence for the population mean μ. is
xbar-tc*s/sqrt(n),xbar+tc*s/sqrt(n)
20-(1.6802*2.2/sqrt(45)),20+(1.6802*2.2/sqrt(45))
19.44897,20.55103
lower limit= 19.44897
upper limit=20.55103
we are 90% confident that the true population mean weight of watermelons lies in between 19.45 pounds and 20.55 pounds.