Question

A marketing research experiment was conducted to study the relationship between the length of time necessary for a buyer to reach a decision (y) and the number of alternative package designs (2, 3, or 4 designs). Remember that s = √MSE. Use the tables below to answer the following questions.

	Estimate	Std. Error	t value	Pr(>|t|)
(Intercept)	3.633	0.865	4.200	0.001
Design	1.700	0.449	3.786	0.001

Observations	s	R-squared	Sxx	mean(x)
15	1.468	0.508	10	3

a) Predict the mean amount of time necessary for a buyer to make a decision if there were 5 package choices. Is this value meangingful? Why or not?
?̂ =  

The prediction   is/ is not  meaningful since ?0 = 5   does/ does not  fall within the range of   length of time/ designs .

b) Find the 95% prediction interval (i.e. confidence interval for predicting) of y when ?0x0 = 4.
?̂ =  
??/2 =  
(  ,  )

c) Is there evidence to support that the correlation coefficient is not equal to 0? Test using ?α = 0.05.
?0:? = < > /=  0
??:? = < > /= 0

Test statistic: t =  
Critical value: ??/2 =  
Decision:   Reject/ Fail to reject  
Interpretation: There   is/ is not  evidence to support that the correlation coefficient is not equal to 0.

Answer 1