Question

The table below shows the birth weight in grams of 12 babies born at 40 weeks to mothers with type I diabetes.

4165

2894

4106

3591

2867

3528

3215

3026

4300

4174

4032

3771

a) Calculate the sample mean and variance for the birth weight in this sample. 


b) Estimate the population mean and variance and compare with the known values μ₀=3525 grams and σ₀=450 grams (the data were actually generated using a normal distribution with these parameter values). Why are your estimates so off? 


c) Use the known population parameters above (μ₀=3525 grams and σ₀=450 grams) to calculate the standard error of the mean (SEM) assuming the CLT applies. 


d) Assuming the CLT applies, indicate the distribution you expect the sample mean to follow and calculate the probability of observing a value equal or higher than the one you determined in (a). 


Answer 1