Two events are mutually exclusive if ________.

a. They are independent

b. they both cannot occur together.

C. the occurrence of one slightly alters the probability of the occurrence of the other.

D. the probability of their joint occurrence equals one.

A frequency distribution is to _____ as a binomial distribution is to______

a. concrete ; discrete variables

b. frequencies; probabilities

c. easy; hard

d. wide range; small range

Captain Kirk and Mr. Spock are engaged in a 3-D backgammon playoff, a game employing 6 dice. Kirk asks Spock the probability of rolling the dice and observing 6 sixes. Assume the dice are not biased and cannot affect each other. Spock's correct a priori response is ____.

A. "insufficient data Captain"

b. (1/6) 6

c. 1/36

d (1/36) 6

If A and B are mutually exclusive and exhaustive, then p(A and B) = ______.

A. 1

B. p(A) + p(B)

c. p(A) + p(B) - p(A and B)

d. 0

The symbol H1 stands for

a. null hypothesis

b. alpha

c. beta

d. alternative hypothesis

An alpha level of .05 indicates that ______

a. the probability of a Type II error is .05

B. the probability of a correct decision is .05

C. 95% of the time, chance is operating

d. if Ho is true, the probability of falsely rejecting it is limited to .05

1. Is it correct to conclude by accepting the H1 when the results of the experiment are significant? Explain.

-no because accepting the H1 means that we have concluded that the iv affects the dv beyond a shadow of a doubt. In fact, if p < .05 there are still possibly 5 chances in 100 that the iv is not affecting the dv. In addition­we don't test the h1 and as such cannot accept it.

2. What does a p value < .05 signify and what is our conclusion when have this?

that there are fewer than 5 chances in 100 that our results are due to chance and as such, this is a low enough probability that we can safely reject the null.

3. Explain how sampling without replacement may also mean that events are dependent. Provide an example.

sampling without replacements means that you take an object and don't put it back b4 taking another. If this happens, then the probability of taking that first object affects the probability of the other objects being taken, which is the definition of dependent events. Eg., if i have 5 (1 blue and 4 red) candies and i eat one blue, that affects the probability that a red one will be the next i eat.

A pop machine with no selection buttons on the front, contains 12 cans of Diet Coke, 10 cans of Coke, and 7 cans of Pepsi. You randomly select 3 cans to purchase. What is the probability that of the three cans, exactly one is Coke and one is Pepsi? (you are going to keep all three cans) (8)

1 2 3

c p d = 10/29 x 7/28 x 12/27 = 840/21924 x 6 = .23

d c p

p d c

p c d

c d p

d p c

It is estimated that 45% of students leave town for Spring Break. 10 students are randomly sampled and surveyed about Spring Break plans. What is the probability that more than half of the sample is leaving town for Spring Break? (8)

Binomial: n=10

p=.45

.1596+.0746+.0229+.0042+.0003

see # 12 on p 238 of your text. (a b and c only) But for subject 1, make Bar 1 = 40 and Bar 2 = 20.

P (9) + p(10) + p(11) + p(12) + p(3) + p(2) +p(1) + p(0)