## statistics exam prep

hello everybody,

i'm preparing for a statistics exam and can't solve the following questions; can anybody help me(please provide explanation)?

1. True or false (why?)

"If one wishes to reduce by 50% the error that can exist in estimating the mean by sample mean, it simply requires that the sample size be doubled"

2. A man is in the process of buying a new car. He has a choice of 3 engine makes, 7 body styles and 10 colors. How many different cars does he have to choose from?

3. A family has two children. What is the conditional probability that both are boys given that at least one of them is a boy?

4. Given a 95% confidence interval for the mean of a population is from 110 to 120. How do you interpret this confidence interval?

5. Consider the following events in the toss of a single die:
A: observe an odd number
B: observe an even number
C: observe a 1 or a 2
a) Are A and B independent? Why?
b) Are A and C independent? Why?

6. Which of the following two events is more likely? Why?
a. Obtaining exactly 3 heads in tossing a fair coin 10 times.
b. Obtaining exactly 3 heads in tossing a fair coin 15 times.