Descriptive Statistics and Interpretation qnt 561

Descriptive Statistics

Deborah Morrison

QNT/561

March, 02, 2016

DAVOR SIJERKOVIC

Descriptive Statistics

Descriptive statistics is defined as a set of short-lived descriptive numbers that sums up a data set, which can be an exemplification of the total amount or just a sample. The instruments used to depict the data set are processes of central tendency and measures of unpredictability or dispersion (Taeuber, 1987). We are comparing two different means. Therefore a t-test is the most appropriate tool to use to measure the central tendencies between the two variables. Because our data is not significantly skewed we used mean and standard deviation to test the hypotheses.

Numeric Variable Average Produce sales for Shop-mart Consumer

Distribution: Not normally distributed.

Sample sales: Shop-mart: 30, 35, 40, 45, 50, 55, 60 Central Tendency: Mean- Shop-mart: $45,000 Median- Shop-mart: $45,000 Mode- Shop-mart: No Mode because each appears equally as often.

Dispersion- Shop-mart: Standard Deviation- 10.8

Number: 7

Min/Max: $30.00 min/ $60.00 max

Confidence Interval: There is no confidence interval because the data is not normal.

Numeric Variable Average Sales for Target Consumer

Distribution: Not normally distributed.

Target: 49, 54, 59, 64, 69, 74, 79

Central Tendency: Mean-Target: $64.00 Median- Target: $64.00 Mode- Target: There is no mode because each number shows up equally as often.

Dispersion: Standard Deviation- 10.8

Number: 7

Min/Max: $49.00 min/ $79.00 max

Confidence Interval: There is no confidence interval because the data is not normal.

Shop-mart/Target Consumer Bar Chart Analysis (See Appendix B)

We are showing the difference between median sales for consumers who purchase produce at Shop-mart versus a consumer that purchase produce at Target. If the two boxes were overlapping then there would not be enough of a difference between them however, since Target is clearly double the sales amount of Shop-mart, the chart shows the difference.

Descriptive Statistics Interpretation

Numeric Variable – Shop-mart (See Appendix C)

Ho: =45

H1: >45

T-test:

T-score: 4.654

P-value: .0017

If p<x, then reject Ho. This shows that the p-value is significantly less than alpha then there is a significant difference between mu and x-bar. Therefore there is a difference between the average annual sales of Shop-mart versus Target shoppers.

References

D'Innocenzio, A. (2012.). Walmart and Target: A tale of two discount chains. In CBS Moneywatch. Retrieved March 02, 2016, from http://www.cbsnews.com/news/walmart-and-target-a-tale-of-two-discount-chains/

Identifying variables and collecting data. (2014,). In StatCrunch. Retrieved March 2, 2016, from http://www.statcrunch.com/profile.php?id=-70685-1_blackboardht_cwi

Taeuber, R. C. (1987). Basic Data: Descriptive Statistics. International Journal of Educational Research, 11(4), 397-401.

Appendix A

Raw data used in the analysis

RQ: Is there a significant difference between the sales of a consumer that purchase produce at Target verses the produce sales of a Shop-mart shopper?

Ho: There is a significant difference between the produce sales of a consumer that shops at Target verses the produce sales of a Shop-mart shopper?

H1: There is not a significant difference between the produce sales of a consumer that shops at Target verses the produce sales of a Shop-mart shopper?

Shop-mart average shopper spends between $30 to $60 and Target on produce suggests that their average shopper spends $64 for produce (D'Innocenzio, 2012).

Several average consumer produce sales from each store is as follows:

Shop-mart: 30, 35, 40, 45, 50, 55, 60

Target: 49, 54, 59, 64, 69, 74, 79

Appendix B

Charts and Tables

Histogram

Two Sample T

μ1 comes to : variance of sample1

μ2 comes to: variance of sample 2

μ1 - μ2 : Difference between the two

Difference Sample Diff. Std. Err. DF L. Limit U. Limit

μ1 - μ2 -19 5.7735027 12 -31.579382 -6.4206183

Scatterplot

Bar Chart

Appendix C

Descriptive Statistics

Ho: μ=45

H1: μ>45

Μ=45 n=7 x̄=64 σ= 10.8

T-test: t=4.654

p=.0017

*if p<x, then we must reject the null hypothesis.