A food company wanted to know if the amount of taste enhancer added to one of its products has any effect. It ran a test by adding eight different amounts and asking a panel of tasters to rank the results. (Considering a scale from 1 to 10, with 1 representing a 'low' rank and 10 a 'high' rank.)

Table 2 Food company data

Test

A

B

C

D

E

F

G

H

Amount of enhancers

22

17

67

35

68

10

37

50

Rank

3

2

8

5

7

1

4

6

See below the corresponding Excel regression output.

a. Comment on the relationship between the amount of enhancer and the ranking by the panel. Clearly justify your claim. 

b. Determine the equation of the regression line that can be used to predict the ranking given the amount of enhancers. Explain the meaning of the regression coefficient and the intercept. Predict the ranking for an amount of 55 enhancers.   

c. Use a significance level of 5% to test whether the ranking is significantly related to the amount of enhancer. What is your conclusion?

d. Explain the relevance of the confidence interval for the conclusion you derived at in (c).