# Statistics test

- In an early study, researchers at a private University found that 33% of the freshmen had received at least one A in their first semester. University administrators have received report that grade inflation may have caused this percentage to increase recently. A random sample of 500 freshmen found that 180 had at least one A in their first semester. Calculate the appropriate test statistic and test the hypotheses related to the concern and test at 5% and 1%.

- A merchant needs a forecast for the sales of a product (in millions). He thinks that the sale is affected by expenditure on advertising (in millions of dollars). Based on the data set with six observations, the summary statistics are given below (X is expense on advertising expenditure in million dollars and Y is number of products sold in millions): ∑X = 24; ∑Y = 42; ∑X2 = 124; ∑Y2 = 338; ∑XY = 196 Find the Intercept and slope, write the Regression Equation, and interpret the results. Make a forecast for the sale of products (in millions) if the advertising expenditure is 5 million dollars. Calculate the correlation coefficient, coefficient of Determination. Verify the relationship between the coefficient of correlation and the coefficient of Determination. Calculate SSE and MSE and standard error of the slope coefficient and perform the test of significance.

- A product rating agency has the following data about the quality score for an electronic product and respective prices for 10 popular brands.

Brand Price Score

A 2900 55

B 2800 54

C 2700 45

D 3500 56

E 3300 54

F 2000 35

G 4200 68

H 3100 56

I 2500 32

J 3000 45

Calculate the Regression coefficients based on the above data and explain what the values indicate. Measure the Goodness of Fit using the Coefficient of Determination and interpret the calculated value with respect to the model’s overall explanatory power. Also check the relationship between R2 and r.

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