Question

The maximum reaction rates (Vmax) for the enzyme invertase were measured from samples at four temperatures. Test the hypothesis that there are no significant differences in the mean invertase reaction rates among temperatures at the 5% level of significance. (8 points)

Vmax for Inveratse (10–3 mM/min)
30C	40C	50C	60C
2.3	2.6	2.9	2.8
2.9	3.2	3.5	3.4
2.2	2.4	4.2	2.6
2.5	3.2	2.6
3.2

7. Report the SS(total) value

a. 4.0500

b.5.5800

c.2.5300

d. 4.1094

8. Report the SS(error) value

a.2.0922

b.2.4950

c.3.4400

d.4.5430

9. Report the MS(group) value

a.0.3592

b.0.5382

c.0.2582

d.0.6526

10. Report the MS(error) value

a.0.3928

b.0.5322

c.0.2078

d.0.1744

11. What is the F-ratio?

a. 2.59

b.3.74

c.4.83

d.5.46

12.What is the F(critical) value?

a.2.97

b.3.49

c.4.83

d.5.46

13. Which of the following Null Hypothesis is true?

a.H0: All sites have equal means

b.H0: Two of the sites have equal means

c. H0:At least one site has a different mean

d. H0: Two sites do NOT have equal means

14. Which of the following Alternate Hypothesis is true?

a.H1:All sites have equal means

b.H1:Two of the sites have equal means

c.H1:At least one site has a different mean

d.H1:Two of the sites do NOT have equal means

15. What is your conclusion?

a.Reject H0

b.Do Not Reject H0

c. All sites have different means

Answer 1

	A	B	C	D
count, ni =	5	4	4	3
mean , x̅ i =	2.620	2.85	3.30	2.93

std. dev., si =	0.421	0.412	0.707	0.42
sample variances, si^2 =	0.177	0.170	0.500	0.173
total sum	13.1	11.4	13.2	8.8	46.5
grand mean , x̅̅ =	Σni*x̅i/Σni =	2.91

square of deviation of sample mean from grand mean,( x̅ - x̅̅)²   0.082   0.003   0.155   0.001  
                   TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =    0.410   0.013   0.620   0.002   1.044708333
SS(within ) = SSW = Σ(n-1)s² =    0.708   0.510   1.500   0.347   3.0647
no. of treatment , k =   4              
df between = k-1 =    3              
N = Σn =   16              
df within = N-k =   12              
                  
mean square between groups , MSB = SSB/k-1 =    0.3482              
                  
mean square within groups , MSW = SSW/N-k =    0.2554              
                  
F-stat = MSB/MSW =    1.3636              
P value =   0.3008              

anova table
	SS	df	MS	F	p-value	F-critical
Between:	1.0447	3	0.35	1.36	0.3008	3.49
Within:	3.0647	12	0.26
Total:	4.1094	15
					α =	0.05
			conclusion :	p-value>α , do not reject null hypothesis

a.H0: All sites have equal means

if alternate true

c.H1:At least one site has a different mean

conclusion :    p-value>α , do not reject null hypothesis            

Please revert back in case of any doubt.

Please upvote. Thanks in advance.