Question

In: Statistics and Probability

explain the difference between the confident interval and the confident level. Then provide an example to...

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.

Solutions

Expert Solution

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.


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