HOMEWORK 4
Introduction to Probability & Sign Test
Note: Carry out all calculations to FOUR decimal places.
1.
(10 pts) A social psychologist believes that women, in general, are less likely to enjoy
rock music. The psychologist recruits 100 participants (50 males and 50 females) to go
to a concert. They are told that they are free to leave whenever they want. He records
the sex of a total of 10 people who end up leaving the concert, as follows:
[M F F F F F F F F F]
a. What is the probability that out of the 10 people who are displeased with the concert,
9 of them are women?
b. What does this say about the psychologist’s belief that women are less likely to enjoy
this particular rock concert?
2. (15 pts) I flip a fair coin 17 times. Answer the following questions:
a. What is the probability of getting 9 heads?
b. What is the probability of getting 2 heads?
c. What is the probability of getting 1 tail?
d. What is the probability of getting 14 or more heads?
e. What is the probability of getting 17 tails?
3. (15 pts) I toss an unfair coin 12 times. This coin is 65% likely to show up heads.
Calculate the probability of the following:
a.
b.
c.
d.
e.
11 heads:
2 or more heads:
7 heads:
9 tails:
8 or less heads:
4. (15 pts) Suppose that you know that a coin you have has a tendency to turn up tails 75%
of the time, and heads 25% of the time. Use the binomial table to calculate the
probability of obtaining
A) 3 heads on three tosses of this unfair coin.
B) at least 2 heads on three tosses of the coin?
C) 1 tail on three tosses of the coin?
5.
(15 pts) I roll a pair of standard dice once. What is the probability that on this roll I
obtain:
a.
b.
c.
d.
A sum of 12
A sum of exactly 2
A sum of exactly 3
A sum less than 12
e. A sum of exactly 4
For the following questions, please use the formal steps of hypothesis testing we covered in
class:
Probability
6. (15 pts) A hockey team is convinced that the coin used to determine the order of
play is weighted. The team captain steals this special coin and flips it 14 times to
evaluate the hypothesis that the coin is weighted, and it shows up heads 12 times.
Test this hypothesis (use alpha=.05).
a. (2 pts) What is the appropriate test?
b. (1 pt) State the null hypothesis:
c. (1 pt) State the alternative hypothesis:
d. (4 pts) Find the critical value:
e. (2 pt) Calculate the obtained statistic:
f. (2 pts) Make a decision:
g. (3 pts) Indicate the probability of every outcome (either on top of each bar
or somewhere separately) and shade in the rejection region below:
Number of Heads
7. (15 pts) A hockey team is convinced that the coin used to determine the order of
play is weighted for heads. The team captain steals this special coin and flips it 14
times to evaluate the hypothesis that the coin is weighted for heads, and it shows
up heads 12 times. Test this hypothesis (use alpha=.05).
a. What is the appropriate test?
b. State the null hypothesis:
c. State the alternative hypothesis:
d. Find the critical value:
e. Calculate the obtained statistic:
f. Make a decision:
g. Indicate the probability of every outcome (either on top of each bar or
somewhere separately) and shade in the rejection region below:
Probability
Number of Heads