An advertising firm wishes to demonstrate to potential clients the effectiveness of the advertising campaigns it has conducted. The firm is presenting data from recent campaigns, with the data indicating an increase in sales for an increase in the amount of money spent on advertising. In particular, the least-squares regression equation relating the two variables cost of advertising campaign (denoted by an x and written in millions of dollars) and resulting percentage increase in sales (denoted by y) for the campaigns is y = 6.15 0.19x , and the standard error of the slope of this least-squares regression line is approximately 0.06.
Using this information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population slope. (Assume that the variable follows a normal distribution for each value of and that the other regression assumptions are satisfied.) Use the level of significance, and perform a two-tailed test.
This solution shows details of a hypothesis test for the slope of a least squares regression line.