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# Confidence Interval for the Population Mean (Essay Sample)

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A: Create and interpret a Confidence Interval for the Population Mean ( CI for µ)
1 Summary Statistics
Price

Mileage

Mean

37533

Mean

4061.667

Standard error

1600.09247

376.3977

Median

38,500

3150

Mode

34500

2000

Standard Deviation

8764.06737

2061.615

Sample Variance

76808876.9

4250256

Quartile 1

30925

2425

quartile 3

44975

5745

Range

28,200

6700

Minimum

21,900

1800

Maximum

50,100

8500

Sum

77105874.1

4287075

Count

30

30

2 Create a 95% Confidence Interval for the Population Mean ( CI for µ)
CI=mean±ta2, n-1 x s√n
Where a=0.05, corresponding to 95% confidence interval
se . standard error is given as s√n
se=8764.067√30

se= 8764.0675.47723= 1600.091
The 95% confidence interval is given as,
37533± t0.05/2,301*1600.091
a= 0.05
t0.05/2,29= 2.04523 since we have 29 degrees of freedom
CI= 37533±2.04523* 1600.091
CI= 37533±3272.55
CI= 34260.44,40805.55
Interpretation of the Confidence Interval
The true value of the unidentified population parameter is located within the confidence interval. A confidence interval is constructed using the sampling distribution of the estimator, in this case the sample mean, to determine the true population mean.
If we take 100 samples and compute a 95% confidence interval for each, then 95 of the intervals will contain the true mean value of the population, which is the population mean mu.

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