Question

In R Studio, 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?

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

Answer 1

solution:

   Here the statistical hypothesis to be tested is as follows,

Null hypothesis: μ = 48

Alternative hypothesis: μ ≠ 48

Where, μ = mean number of breeding ponds ,

R - code is as follows;

Mu= 48 # True or given mean
Breeding=c(61,70,61,113,92,100,102,66,64,18)
Xbar= mean(Breeding) # sample mean
Xbar
SE=sd(Breeding) # Sample standard deviation/ standard error
SE

# Here test statistic computed as follows,
  
Tcal= (Xbar- Mu)/SE
Tcal
Ttab=qt(0.975,9) # Tabulated value of t-probability distribution at 9 d.f. and 95% level of significance.
Ttab

# Since Tcal < Ttab , we may accept null hypothesis.

R-code out put ;-

> Mu= 48       # True or given mean
> Breeding=c(61,70,61,113,92,100,102,66,64,18)
> Xbar= mean(Breeding)      # sample mean 
> Xbar
[1] 74.7
> SE=sd(Breeding)           # Sample standard deviation/ standard error 
> SE
[1] 27.79708
> 
> # Here test statistic computed as follows,
>   
> Tcal= (Xbar- Mu)/SE
> Tcal
[1] 0.9605325
> Ttab=qt(0.975,9)     # Tabulated value of t-probability distribution at 9 d.f. and 95% level of significance.
> Ttab 
[1] 2.262157
> 
> # Since Tcal < Ttab , we may accept null hypothesis.

Hence we may claim that the mean number of breeding ponds found in NSW is same as the mean number found in the Victorian surveys.

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