# Confidence Interval for the Population Mean (Essay Sample)

Use your data set and summary statistics from Part 1 of the Project, to answer the following questions. Put your results in a semi-professional looking report. Make sure to include your name, date, title, page numbers, etc. If there were any invalid responses in your data, you will want to eliminate these responses from your sample and mention that this was done in the intro or conclusion of your paper. For this project, use the PRICE variable and your qualitative variable that isn′t color (either: sustained damage or not, convertible or not, or single owner or not). A. Create and Interpret a Confidence Interval for the Population Mean (CI for µ) List the summary statistics (i.e. sample average, sample standard deviation, sample size, and anything else you would like to include) for the PRICE variable. Create a 95% CI for the true mean of your PRICE variable. (Note: you do not need to show your work). Practically interpret this confidence interval. Theoretically interpret the phrase “95% confident.” B. Create and Interpret a Confidence Interval for p (CI for p) State the number of vehicles who are in each of the two groups for your qualitative variable that isn′t color and the total sample size. For example, if your non-color qualitative variable was single owner or not single owner, then I would state something like, ″30 Camaros were sampled. Of those 30 Camaros, 17 had a single owner and 13 had more than one owner″). Pick one of the levels as a ″success″ then calculate and interpret that value. Optionally, you may also want to calculate 1 - . Create a 95% CI for p. (You do not need to show your calculations) Practically interpret this confidence interval. Theoretically interpret the phrase “95% confident.” C. Optional You may wish to include an introduction, conclusion, check your assumptions, etc. However, this will not be a part of your grade.

source..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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