Question

(2) Does the number of tadpoles vary between the relative altitudes at which the sites were located? If so, which of the altitude level means are significantly different? . The mean number of breeding ponds was found to be 48. The researcher wants to know if the mean number of breeding ponds found in NSW is different from the mean number found in the Victorian surveys?

Site	Rain	Temp	Altitude	Tadpoles	Breeding
1	769.77	22.37	Low	97	61
2	664.85	19.46	Low	86	70
3	807.13	23.17	Low	104	61
4	620.05	17.85	Low	117	113
5	673.21	20.29	Low	98	92
6	734.18	20.58	Low	88	100
7	526.62	16.29	Low	95	102
8	647.86	18.51	Low	38	66
9	672.3	20.13	Low	64	64
10	666.67	18.91	Low	57	18

Answer 1

breeding data-

61
70
61
113
92
100
102
66
64
18

Ho :   µ =   48              
Ha :   µ ╪   48       (Two tail test)      
                      
Level of Significance ,    α =    0.050              
sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   27.7971              
Sample Size ,   n =    10              
Sample Mean,    x̅ = ΣX/n =    74.7000              
                      
degree of freedom=   DF=n-1=   9              
                      
Standard Error , SE = s/√n =   27.7971   / √    10   =   8.7902  
t-test statistic= (x̅ - µ )/SE = (   74.700   -   48   ) /    8.7902   = 3.037

                      
  
p-Value   =   0.0141   [Excel formula =t.dist(t-stat,df) ]          
Decision:   p-value<α = 0.05 , Reject null hypothesis                   
Conclusion: There is enough evidence to conclude that   mean number of breeding ponds found in NSW is different from the mean number found in the Victorian survey