Confidence intervals question

Nephew

Hey guys. I've an exam coming up soon in financial maths and I am trying to prepare by doing a few practice questions, but unfortunately I am dire at maths. I would be forever grateful if anyone could answer this question and show me how you did it, formulas etc.

Question:
An investigation was carried out into part-time working by full-time third level students in Dublin. In the study 200 males and 150 females were randomly selected. The results of the study are shown in the following table.

Males: 200
Number with part time work:160
Average hours work each week: 12
Standard deviation: 5

Females: 150
Number with part time work:105
Average hours work each week: 10
Standard deviation: 5


1) Calculate95% confidence intervals for the average number of hours worked per week by Males and Females ( two intervals).

2) From the inspection of your intervals in ( 1) does it appear likely that the True Average is the same for both males and females? Explain your conclusion.

3) What sample size would be required to achieve precision of +- 0.4 hours
and 99% confidence when estimating average number of hours worked per week by males ?

4) Calculate a 95% confidence interval for the overall percentage of students
with part-time work.

5) What sample size would be required to achieve precision of +-3% and
95% confidence, when estimating the overall percentage?

6) When should Population size be taken into account in the calculation of sample size?

Thanks

nothing

Have you not even tried any of these?

Nephew

I tried it but I was getting nowhere tbh.