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, the cost of the advertising campaign (denoted by x and written in millions of dollars) and the resulting percentage increase in sales (denoted by Y), for the l campaigns is y = 6.43 + 0.1x. The standard error of the slope of this least-squares regression line is approximately 0.09.
Using this information, test for a significant linear relationship between these two variables by conducting a hypothesis test regarding the population slope Β. Assume that the variable Y follows a normal distribution for each value of x and that the other regression assumptions are satisfied. Use the 0.05 level of significance and perform a two-tailed test. Then fill in the table below.
The null hypothesis:
The alternative hypothesis:
The type of test statistic:
The value of the test statistic: (Round to at least three decimal places.)
The p-value: (Round to at least three decimal places.)
Based on the data, we conclude (using the 0.05 level) that there is a significant linear relationship between the cost of the advertising campaign and the resulting percentage increase in sales.
