Question

Q07. An ANOVA examining three different blanching processes to determine which is best in terms of vitamin A retention (mg/100mg) yields an F statistic with an associated P-value of < .001. Therefore, at α = .05 we

I. fail to reject the null hypothesis.
II. reject the null hypothesis.
III. conclude that mean vitamin A retention amounts are not all equal across the different blanching processes

a) II only

b) I only

c) both II and III

d III only

e) both I and III

Q08. Given that the sum of squares for between-groups (SSB) for an ANOVA  F-test is 9,000 and there are four total groups, find the mean square for between-groups (MSB)

a) 1,800

b) 1,500

c) 2,250

d) 3,000.

Q09. An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of 20 recently hired sales trainees were randomly assigned to one of four different "home rooms" - five trainees per room. Each room is identical except for wall color. The four colors used were light green, light blue, gray and red. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to the four room colors. At the end of the training program, the attitude of each trainee was measured on a 60-point scale (the lower the score, the poorer the attitude). Give the null hypothesis

a) The five trainees in one room have the same mean attitude score as the five in a different room

b)The four rooms with different colors have the same mean attitude score.

c) The 20 sales trainees have the same attitude score

d) The four rooms with different colors do not all have the same mean attitude score

Q10. A certain HMO is attempting to show the benefits of managed care to an insurance company. The HMO believes that certain types of doctors are more cost-effective than others. One theory is that certification level is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the HMO obtained independent random samples of 21 physicians from each of the three certification levels—Board certified (C); Uncertified, board eligible (E); and Uncertified, board ineligible (I)—and recorded the total per-member, per-month charges for each (a total of 63 physicians). In order to compare the mean charges for the three groups, the data will be subjected to an analysis of variance. Give the degrees of freedom appropriate for conducting the ANOVA  F-test. [Note: numerator df = between-groups df, denominator df = within-groups df]

a) numerator df = 61, denominator df = 3

b)numerator df = 61, denominator df = 2

c) numerator df = 2, denominator df = 60

d) numerator df = 3, denominator df = 60

Answer 1

Q07: c) both II and III

Here, the p-value <0.05(Level of significance and hence the Null hypothesis is rejected).

Q08: d) 3,000.

Number of groups=4 and hence the df=4-1=3. Therefore MS=9000/3=3000

Q09: b)The four rooms with different colors have the same mean attitude score.

In an ANOVA the Null hypothesis is  

Q10: c) numerator df = 2, denominator df = 60

The total df=63-1=62, The groups df=3-2=2 and hence within groups=62-2=60. Therefore numerator=2 and the denominator=60)