Question

One of the assumptions we sometimes need to make when performing statistical inferences is that the response variable in the population has a Normal distribution. Is it possible to check that this assumption is satisfied?

No - we can't really check this assumption since all data will look perfectly bell-shaped and symmetric, even if the population was not Normal.

Yes - we can be absolutely sure the population was Normal if a plot of the data has no major outliers.

No - we can't really check this assumption since we don't have the whole population, but the t distribution is robust to modest departures from Normality, so we can use it if a plot of the data has no major outliers.

Yes - we can be absolutely sure the population was Normal if a plot of the data looks roughly bell-shaped and symmetric.

Yes - we can be absolutely sure the population was Normal if a plot of the data looks perfectly bell-shaped and symmetric.

Answer 1

No - we can't really check this assumption since we don't have the whole population, but the t distribution is robust to modest departures from Normality, so we can use it if a plot of the data has no major outliers.

Option C is correct.