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 20 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 31.81 kg and the average weight of two week old pups was 36.19 kg. The variance of the difference between the one week and two week pup weights was found to be 14.23.
H₀: 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?

a) Yes, we reject the null hypothesis
b)No, we fail to reject the null hypothesis

Answer 1

Answer:

stated hypothesis

H₀: μ₁ = μ_{2 i.e} there is no significant difference in the weight of one week old grey seal pups versus two week old pups.
H_a: μ₁ ≠ μ_{2 i.e} there is a significant difference in the weight of one week old grey seal pups versus two week old pups.

NOW with the help of minitab software we apply Two-Sample T-Test

Method

μ₁: mean of Sample 1

µ₂: mean of Sample 2

Difference: μ₁ - µ₂

Equal variances are assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Sample 1	20	31.81	3.77	0.84
Sample 2	20	36.19	3.77	0.84

Estimation for Difference

Difference	Pooled StDev	90% CI for Difference
-4.38	3.77	(-6.39, -2.37)

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ ≠ 0

T-Value	DF	P-Value
-3.67	38	0.001

• so the test statistic = -3.67
• 90 % confidence interval = (-6.39, -2.37)
• a) Yes, we reject the null hypothesis { because the p value is 0.001 < 0.1 at 10 % level of significance it gives the srong evidence against the null hypotheis since we can reject the null hypotheis therefore we can conclude that there is a significant difference in the weight of one week old grey seal pups versus two week old pups.