You will prepare and submit a term paper on 3 questions. Your paper should be a minimum of 500 words in length. STATISTICS Q1. According to the statistical analysis of the correlation of the forms of consumer installment credits, the following result from the table gives the correlation levels.

Table 1: Correlations

Gas Cards

Travel & Enter. Card

Bank Credit Card

Retail Card

Total Credit Card

Total Installment Card

Gas Cards

Pearson Correlation

1

.775**

.750**

.784**

.781**

.736**

Sig. (2-tailed)

.005

.008

.004

.005

.010

N

11

11

11

11

11

11

Travel Enter. Card

Pearson Correlation

.775**

1

.960**

.975**

.973**

.958**

Sig. (2-tailed)

.005

.000

.000

.000

.000

N

11

11

11

11

11

11

Bank Credit Card

Pearson Correlation

.750**

.960**

1

.978**

.994**

.996**

Sig. (2-tailed)

.008

.000

.000

.000

.000

N

11

11

11

11

11

11

Retail Card

Pearson Correlation

.784**

.975**

.978**

1

.995**

.981**

Sig. (2-tailed)

.004

.000

.000

.000

.000

N

11

11

11

11

11

11

Total Credit Card

Pearson Correlation

.781**

.973**

.994**

.995**

1

.993**

Sig. (2-tailed)

.005

.000

.000

.000

.000

N

11

11

11

11

11

11

Total Installment Card

Pearson Correlation

.736**

.958**

.996**

.981**

.993**

1

Sig. (2-tailed)

.010

.000

.000

.000

.000

N

11

11

11

11

11

11

**. Correlation is significant at the 0.01 level (2-tailed).

The correlations table above represents the data from year 1 to year 11. Using Pearson’s correlation, the relationship among the different forms of the consumer installment cards is highly positive. The correlation between the gas card and travel entertainment card, using the Pearson’s correlations is 0.775 from the 1st to the 11th year. Travel and entertainment card and the Bank credit card is 0.960 positively correlated to each other. In the same manner, the bank credit and retail credit cards are 0.978 positively correlated. As shown in the table above, the relationships among the various forms of consumer installment cards are highly correlated positively.

Q2. Calculate the mean average miles per gallon. Compute the sample variance and sample standard deviation. Determine the most appropriate statistical test using the 0.5 significance level.

Table 2: Descriptive Statistics

N

Minimum

Maximum

Mean

Std. Deviation

Variance

Miles per Gallon

24

21.90

35.10

28.3792

2.97643

8.859

Valid N (list wise)

24

According to the table above, the mean average miles per gallon are 28.3792 when the total sample of purchasers is 24. In the same manner, out of the 24 sampled data, the sample variance is 8.859 whereas the sample standard deviation is 2.97643 as shown in the SPSS output table above.

Under the sample of 24, which is below 30, the most appropriate statistical test, using the 0.5 significance level is the student’s t-distribution test. Under this test, the sample must be 30 or less, and the arithmetic mean is not normally distributed.

Q3

Interpret the output, examining group differences for purchase intentions. The three groups refer to consumers from three states: Illinois, Louisiana, and Texas.

Tests of between -subjects’ effects

Dependent variable: Int2

source Type III sum of squares df mean square f sig.

Corrected model 6681.746 2 3340.873 3.227 0.043

Intercept 308897.012 1 308897.01 298.3230.000

State 6681.746 2 3340.873 3.227 0.043

Error 148068.543 143 1035.444

Total 459697.250146

Corrected Total 154750.289145

R squared=0.043 (Adjusted R squared=0.030)

According to the output table above, the Adjusted R squared is 0.030, meaning that only 3% of the variables explain the dependent variable Int. 2. The adjusted R squared helps in predicting how the regression model predicts responses for the explained observations. In this case, it is the fraction by which the variance of the errors that depends on the sum of squares is less than the variance of the dependent variables. Thus, as argued above, only 3% of the independent variables can predict the dependent variable statistically.

When the ANOVA test is run in determining the means among populations, the f statistical value versus the critical value are determined. Under the corrected model, the f statistics is 3.227. Under the assumptions of the hypothesis tests, when the f statistic in attest is lower than the critical f value, then the null hypothesis is rejected. The value obtained means that under the purchase intensions implied by the data above, the null hypothesis is accepted and the independent variables in the states sampled explain the purchase variations.

Also as shown in the second table, the means of the states in terms of consumptions are 37.0.18, 50.357, and 51.459 for the states IL, LA, and TX respectively. The standard error is also 4.339, 4.965, and 4.597 respectively as shown in the table below.

Law

Dependent Variable: int2

95% confidence interval

State Mean std. Error Lower bound Upper bound

IL37.018 4.339 28.441 45.595

LA50.357 4.965 40.542 60.172

TX51.459 4.597 42.373 60.546

There is a higher mean difference in terms of consumers from Texus, then to Louisiana, and finally from Illinois according to the table above. The standard error measures the accuracy of the figures. The smaller the value of the standard error, the closer the value obtained from the regression model. The above standard errors, 4.339, 4.965, and 4.597 are fair enough to show that the estimated values of the dependent variable, purchase intentions in the three states are close to reality.

Reference

Zikmund, W. G., Babin, B. J., Carr, J. C., & Griffin, M. (2013). Business research methods (9th edition). Mason, OH: South-Western.