At a hospital in southern Sweden, 32 children are born one night

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At a hospital in southern Sweden, 32 children are born one night. The mean weight is x ? = 3.2 kg and the sample standard deviation s₁ = 0.8 kg. At a hospital in northern Sweden, 6 children are born the same night with an average weight of y ? = 4.0 kg and a standard deviation of s₂ = 0.7.

Can it be argued from this that there is a significant average difference between births (in terms of weight) in hospitals? Perform a test under appropriate normal distribution assumptions (specify these accurately) at significance level 5%