An advertising firm wishes to demonstrate to potential clients the effectiveness of the advertising campaigns it has conducted. The firm is presenting data from 12 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 x and written in millions of dollars) and resulting percentage increase in sales (denoted by y) for the 12 campaigns is y = 6.18 +0.14x, and the standard error of the slope of this least-squares regression line is approximately 0.10. Using this information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population slope B₁. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.10 level of significance, and perform a two-tailed test. Then complete the parts below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H₁. Ho H₁ :D (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Based on the data, can we conclude (using the 0.10 level) that there is a significant linear relationship between the cost of the advertising campaign and the resulting percentage increase in sales? Yes No В X Olo O
An advertising firm wishes to demonstrate to potential clients the effectiveness of the advertising campaigns it has conducted. The firm is presenting data from 12 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 x and written in millions of dollars) and resulting percentage increase in sales (denoted by y) for the 12 campaigns is y = 6.18 +0.14x, and the standard error of the slope of this least-squares regression line is approximately 0.10. Using this information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population slope B₁. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.10 level of significance, and perform a two-tailed test. Then complete the parts below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H₁. Ho H₁ :D (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Based on the data, can we conclude (using the 0.10 level) that there is a significant linear relationship between the cost of the advertising campaign and the resulting percentage increase in sales? Yes No В X Olo O
ChapterP: Prerequisites
SectionP.6: The Rectangular Coordinate System And Graphs
Problem 2ECP
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Transcribed Image Text:An advertising firm wishes to demonstrate to potential clients the effectiveness of the advertising campaigns it has conducted. The firm is presenting data from
12 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 x and written in millions of dollars) and resulting percentage increase in
sales (denoted by y) for the 12 campaigns is y = 6.18 +0.14x, and the standard error of the slope of this least-squares regression line is approximately 0.10.
Using this information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population slope B₁.
(Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.10 level of
significance, and perform a two-tailed test. Then complete the parts below.
(If necessary, consult a list of formulas.)
(a) State the null hypothesis and the alternative hypothesis H₁.
0
H₁ :0
(b) Determine the type of test statistic to use.
(Choose one)
(c) Find the value of the test statistic. (Round to three or more decimal places.)
Ho
:
(d) Find the p-value. (Round to three or more decimal places.)
(e) Based on the data, can we conclude (using the 0.10 level) that there is a
significant linear relationship between the cost of the advertising campaign
and the resulting percentage increase in sales?
Yes No
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|x
X
O<O
×
Р
0=0
☐#0
н
OSO
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