Question

Grey seals are capital breeders and stay with their pups until they are weaned. A group of researchers on Sable Island are interested in seeing whether there is a significant difference in the weight of one week old grey seal pups versus two week old pups. They measured the weight of 29 one week old pups, then weighed those same pups again one week later. The researchers found the average weight of adult female grey seals was 245.06 kg, the average weight of one week old pups was 34.51 kg and the average weight of two week old pups was 35.70 kg. The variance of the difference between the one week and two week pup weights was found to be 22.92.

Which of the following would be the reasearcher's correct null hypothesis?

H₀: μ₁ = μ₂ = 30
H₀: μ₁ ≠ μ₂
H₀: μ₁ = μ₂
H₀: μ₁ < μ₂

Which of the following is the correct alternative hypothesis?

H_a: μ₁ ≠ μ₂
H_a: μ₁ = μ₂
H_a: μ₁ < μ₂
H_a: μ₁ > μ₂

Calculate the test statistic

Calculate the 90 % confidence interval for the difference in seal pup weights.

Upper Limit Lower Limit

Do we reject the null hypothesis at a significance level α = 0.1?

Yes, we reject the null hypothesis
No, we fail to reject the null hypothesis

Answer 1

H₀: μ₁ = μ₂

H_a: μ₁ ≠ μ₂

Level of Significance ,    α =    0.1
      
      
mean of sample 1,    x̅1=   34.510
      
mean of sample 2,    x̅2=   35.700
      
mean of difference ,    D̅ =    -1.1900
      
std dev of difference , Sd =        4.7875

sample size ,    n =    29          
Degree of freedom, DF=   n - 1 =    28   and α =    0.1  
t-critical value =    t α/2,df =    1.7011   [excel function: =t.inv.2t(α/2,df) ]      
                  
std dev of difference , Sd =        4.7875          
                  
std error , SE = Sd / √n =    4.7875   / √   29   =   0.8890
margin of error, E = t*SE =    1.7011   *   0.8890   =   1.5123
                  
mean of difference ,    D̅ =   -1.190          
confidence interval is                   
Interval Lower Limit= D̅ - E =   -1.190   -   1.5123   =   -2.7023
Interval Upper Limit= D̅ + E =   -1.190   +   1.5123   =   0.3223
                  
so, confidence interval is (   -2.70   < µd <   0.32   )  

0 LIES IN THE NTERAVL

SO,

No, we fail to reject the null hypothesis

..............

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