🚀 go-pugleaf

i really need help in the following statistics problems. hopefully you
can answer these within 8 hours of my posting this, so i can get it
before i leave for home: it is due tommorow, and i have barely completed
half of it.

Q4. A survey of 100 retailers revealed that the mean after-tax profit
was $75000. If we assume that the population standard deviation is
$20000, find the 96% confidence interval of the mean after-tax profit
for all retailers.

Q5. For a given population with standard deviation = 11.4kg, we want to
test the null hypothesis mean does not = 67.3kg against the alternative
hypothesis mean does not = 67.3 on the basis of a random sample size n =
64

a.  If the null hypothesis is rejected when x-bar (i think that's the
mean) < 65.1kg, or x-bar > 69.5kg, what is the probability of a Type I
error?

b.  If in reality mean = 67.0kg, what is the probability of a Type II
error?

Q6.  Employees in a large comapany  are entitled to 15-minute coffee
breaks. A random sample of the duration of coffee breaks for 10
employees was taken with the times shown below. Assuming that the times
are normally distributed, is there enough evidence at the 5%
significance level to indicate that on average employees are taking
longer coffee breaks than they are entitled to?

  12,16,14,18,21,17,19,15,18,16


Q7.  A statistics lecturer wants to know if there is a difference in the
level of understanding of statistics between male and female students.
The lecturer takes a sample of 50 male students and 40 female students
and found the following results. The males averaged 65% with a standard
deviation of 5.48% while the females averaged 70% with a standard
deviation of 8.25%. Can the lecturer conclude at the 5% level of
significance that on average females understand statistics better than
males?

I would really, really appreciate anyone who can help me out. I mean it!
I am desperate! I beg of you! Joy Debnath.