1) A financial analyst assumes that the average value of invoices issued by the company he works for is below 20 million lei / invoice

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1) A financial analyst assumes that the average value of invoices issued by the company he works for is below 20 million lei / invoice. To test this hypothesis, he randomly selects 48 invoices issued in the last month and records their values. Following the data processing, it is obtained:; , where xi is the value of the invoice i. Is the analyst right? (confidence level is 99%).

(2p)

 

2. To decide the location of a new store, the manager of a supermarket chain conducts a study on the following variables: gross annual profit (hundreds of euros), average income of residents in the area (hundreds of euros) and the number of competitors in a radius of a kilometer. After recording and processing the data recorded from 15 supermarkets and assuming a linear dependence between the variables considered, the following results were obtained using the Regression module in EXCEL:

 

Regression Statistics
Multiple R	….
R Square	….
Adjusted R Square	0,423
Standard Error	….
Observations	15

 

ANOVA
	df	SS	MS	F
Regression	…	…	…	…
Residual	…	…	625,607
Total	…	15173,378

 

 

 

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	….	133,661	-0,899	0,386	…………	………….
REVENUE	….	3,538	3,316	0,006	………...	……….....
COMPETITORS	-13,886	10,134	….	0,196	…………	………….

 

a) Fill in the dotted spaces in the ANOVA table, write the regression equation that models the connection between the variables and interpret the values ??of the regression coefficients. (1,5p)

b) Test the statistical significance of the last parameter of the model (β2) and determine and interpret its confidence interval. (1p)

c) Measure the intensity of the connection between the three variables with an appropriate indicator; test the statistical significance of the indicator used. (1p)

 

3. A producer of apple juices has made a new product: liquid concentrate. This new product has the following advantages over the old product: it has at least as good quality and significantly lower cost. To decide which of the two advantages to focus its marketing strategy on, the director of this department conducted a study in two cities. In City A, the advertising campaign focused on the quality of the new product. In city B, the advertising campaign focused on the lower price of the new product. In all three cities, the number of pieces sold in 5 working days of a week was registered.

 

QUALITY:	80	63	77	71	67
PrICE:	67	53	44	59	60

 

The Marketing Director would like to know if there are significant differences between the number of pieces sold, on average per week, in the three cities after the end of the advertising campaign, considering a significance level of 5%. (1.5p)

 

4. The processing of the registered data regarding the salaries of the 10 employees of a travel agency allowed the establishment of the following results:

 

Residuals Sample Variance 59,878 Kurtosis 1,29976 Skewness 1,193 Sum 181 Count 10

Determine and interpret the normality of errors using the Jarque-Berra test. Write the hypotheses of the test. (2p)