Question

If p-value is 0.11 the null hypothesis can be rejected at a = .05. the null hypothesis can be rejected at a =.10. the null hypothesis can be rejected at a =.01. none of the above. 问题8 19 The test statistic for testing significance of the one regression coefficient follows Normal Distribution. Student's t-distribution. O F distribution. Chi-squared distribution. 问题9 19 The test statistic for testing significance of the overall regression model follows Normal distribution. Student's t-distribution. F distribution. Chi-squared distribution. 问题 10 19 Ý = 7 - 6x + 5P where X is advertising in hundreds of dollars ($100), P is Price in tens of dollars ($10) and Y is Sales in number of pieces. If Advertising increases by 1 dollar, sales decrease by 6 pieces. Advertising increases by 100 dollars, sales increase by 6 pieces. Advertising increases by 100 dollars, price increase by 50 dollars.

Answer 1

1.Option 4: none of the above

When p-value is less than α , null hypothesis is rejected at α level of significance. But in the given options all the α values are less than the given p-value. This indicates that the absolute value of the statistic is less than the critical value and the statistic lies in the acceptance region. Thus null hypothesis cannot be rejected at 5%, 10% and 1% level of significance.

2. Option 2: Student's t-distribution

For testing the statistical significance of one regression coefficient student's t-distribution is used. If the statistic's absolute value is greater than the critical value the we observe α is greater than the p-value. Hence the null hypothesis of the regression coefficient=0, is rejected and the coefficient is statistically significant. The reverse is also true when α is less than the p-value.

3. Option 3. F-distribution

Similarly for the overall significance of the model F-distribution is used. If the F statistic lies is the rejection zone then we conclude each of the explanatory variables used in the model has statistically significant impact on Y or dependent variable.

4. Option 1: Advertising increases by 1dollar, sales decrease by 6 pieces

Slope coefficient of X is -6. This shows negative relation between variables X and Y. As X is the dependent variable, it's unit increase cause (6×1) units decrease in Y (as the sign of the coefficient is negative).