that's the context of the questions below:

"The weight of passengers that fly from Lisbon to Oporto and vice versa is a Normally distributed variable.

A sample of 20 weights was randomly selected from the corresponding statistical population: its mean value was computed (68.95 kg) as well as its standard deviation (3 kg). 12 of these weights are from female."

12 out of the 20 weights belong to female (the other 8 to male, of course).

For the purpose of describing the proportion of male let us consider a Xrandom variable(Bernoulli) such that if the weight belongs to a male X=1, if not then X=0.

The proportion of male is then a random variable:

the question I need to answers are

1) What is the 90% confidence interval lower limit for the mean weight () ? (2 decimal digits)

2) For the purpose of rejecting Ho:68 kg, what is the the critical value for a 0.05 significance level? (2 decimal digits)

3) For the purpose of rejecting Ho:68, What is the critical value for a 0.10 significance level? (2 decimal digits)

4)So, about the previous 2 tests...

Select one or more:

a.

at a 0.05 significance level we reject Ho

b.

at a 0.05 significance level we have no reasons to reject Ho

c.

at a 0.10 significance level we reject Ho

d.

at a 0.10 significance level we fail to reject Ho