For Exercises 31–34, assume that the data are independently drawn random samples from normal populations.

  1. Verify the equal-variance assumption.
  2. Calculate the following measures:
    1. and
    3. SSTR
    4. SSE
    5. SST
    6. MSTR
    7. MSE
  3. Construct the ANOVA table.
  4. Perform the appropriate one-way ANOVA using level of significance .

Question 12.31

cafeanova

31. Student-Run Café Business. In Example 8 in Chapter 2, we looked at data from a student-run café business. The table contains the number of food items sold per day.

Wraps Muffins Chips
12 6 7
13 3 16
19 10 8
5 1 4
22 8 10

12.1.31

(a)

image

The smallest standard deviation is 3.65, which is the standard deviation for muffins. Twice 3.65 is 7.30. All other standard deviations are less than 7.30, so the equal variance requirement is satisfied.

(b) (i) , (ii) (iii) SSTR = 187.6 (iv) SSE = 308 (v) SST = 495.6 (vi) MSTR = 93.80 (vii) MSE = 25.67 (viii)

(c)

image

(d) ;

: Not all the population means are equal.

Reject if the .

.

.

The is not . Therefore we do not reject . There is not enough evidence to conclude at level of significance that the population means of the number of different types of food items are not all equal.