19
Question Homework If the odds are 18 to 5 against success, then the probability of success is:
Answer
5/23 = 21.74%
5/18 = 27.78%
5/13 = 38.46%
13/18 = 72.22%
18/23 = 78.26%
Question
A six sided die (like with a Monopoly or Yahtzee game) is put into a microwave on low power in hopes of making it no longer
be fair. The chances of each side are now:
P(1)=0.1 P(2)=0.15 P(3)=0.15 P(4)=0.15 P(5)=0.15 P(6)=?
What is the probability of a 6?
Answer
Question W hich of the following is a valid probability model?
Answer
P(A)=0.6 P(B)=0.5 P(C)=-0.1
P(A)=1.0 P(B)=0.0 P(C)=0.0
P(A)=0.3 P(B)=0.3 P(C)=0.3
P(A)=0.25 P(B)=0.25 P(C)=0.6
0.05
0.10
0.20
0.25
0.30
Homework 20
Question
70% of students in a class are from in-state. 60% of students in a class are female. 45% of the students are in-state females.
W hat percent of students are from out-of-state?
Answer
Question W hat percent are either in-state or female (or both)?
Answer
15%
30%
35%
42%
85%
Question W hat percent are out-of-state females?
Answer
15%
30%
35%
42%
85%
15%
30%
35%
42%
85%
Homework 21
Question A dart player has a 30% chance of getting a bull's-eye on the first throw. If the first throw is a bull's-eye they have a
45% chance of getting one on the second throw. If the first throw didn't hit the bull's-eye they have a 15% chance of getting
one on the second throw.
What is the probability of getting at least one bull's eye?
Answer
0.27 = 27%
0.4 = 40%
0.405 = 40.5%
0.595 = 59.5%
0.6 = 60%
0.73 = 73%
Question W hat is P(missing bull's-eye on second | hit bull's-eye on first) ?
Answer
0.15 = 15%
0.165 = 16.5%
0.3 = 30%
0.45 = 45%
0.55 = 55%
0.85 = 85%
Question A dart player has a 30% chance of getting a bull's-eye on the first throw. If the first throw is a bull's-eye they have a
45% chance of getting one on the second throw. If the first throw didn't hit the bull's-eye they have a ____% chance of getting
one on the second throw.
If the second throw is independent of the result of the first throw, what value would have to go where the blank is?
Answer
0%
15%
30%
45%
55%
70%
85%
Homework 22
Question
The worker at the drive-in window at McDonald's has an 80% chance of asking the customer if they would like a mocha. If the
customer is asked, there is a 15% chance they will order one. If the customer is not asked, there is a 10% chance they will
order one.
What percent of McDonald's drive-in customers will order a mocha?
Answer
8%
10%
12%
14%
15%
25%
Question
55.3% of students at USC are female. 72.2% of students at USC are undergraduates. 38.7% are both undergraduate and
female.
What percent of students at USC are neither undergraduates nor female?
Answer
11.2%
27.8%
39.9%
44.7%
61.3%
Question
In most dart games the player throws three darts. Say the chance of the first one being a bull's-eye is 30%. After that, if the
previous one was made the chance of making the next is 45%. If the previous one was missed the chance of making the next
is 15%.
What is the chance of making all three bull's eyes?
Answer
1.2%
2.025%
4.05%
6.075%
13.5%
20.25%
Homework 23
Question
If a die is fair, it should have a 1/6 (approximately 0.1667) chance of showing a six each time it is rolled. If the die is rolled
500 times, the sampling distribution of the percent of sixes will be approximately normal with mean 0.1667 and standard
deviaiton 0.0167.
Approximately what chance is there of seeing 0.15 or fewer (15% or less) sixes in 500 rolls?
Answer
0.025
0.16
0.34
0.68
0.84
Question
Consider the probability distribution in problem 20.16 (and ignore the fact that rounding error makes the total probability = 1.01,
and that the last category is actually "7 or more").
What is the expected family size?
Answer
2.38
2.87
3.04
3.12
3.23
3.81
Question
Approximately 51% of children born are male, and approximately 49% are female. Imagine that a psychic offers to predict the
sex for $10, with a money back guarantee. If they always predicted male, what would the expected profit be on each
"prediction"?
Answer
$0.20
$4.90
$5.10
$10.00
Homework 24
Question The New York Timesand CBS News conducted a nationwide poll of 1048 randomly selected 13- to 17- year olds.
Of these, 692 had a television in their room. What is the approximate 90% confidence interval for the percent of all 13- to 17year olds who have a TV in there +/- room?
Answer
.398 .025
.398 +/- .030
.398 +/- .033
.660 +/- .024
.660 +/- .029
.660 +/- .031
Question
The Consumer Reports Sentiment Index measures the percentage of how many consumers are doing better than a year ago.
The most recent survey reported that 45.0% in the sample were doing better with a 95% margin of error of +/- 3.2%. So the
95% confidence interval would be .450 +/- .032.
What values must they have used for z* and sqrt(phat(1-phat)/n) to get that +/- 0.032 ?
(Hint: Even if this doesn't look quite as straight forward as question 1, this question is still just using the table and formulas 465
and 466).
Answer
1.64 and 0.0195
1.64 and 0.2744
1.96 and 0.0163
1.96 and 0.2296
2.58 and 0.0124
2.58 and 0.1744
Question
If consumer reports had decided to use a 99% confidence interval, what would it have been?
(Hint: This problem uses your answer from number 2 and the table and formulas from page 465 and 466.)
Answer
.450 +/- .032
.450 +/- .042
.450 +/- .050
.450 +/- .592
Homework 25
Question
Consider the set-up described in problem 22.14. Let p-hat be the percentage of students in your sample who identify
themselves as liberal, and p be the percentage of all students at USC who identify themselves as liberal.
What are the null and alternate hypotheses for this situation?
Answer
Ho: p-hat=0.286 and Ha: p-hat is not equal to 0.286
Ho: p-hat is not equal to 0.286 and Ha: p-hat=0.286
Ho: p=0.286 and Ha: p is not equal to 0.286
Ho: p is not equal to 0.286 and Ha: p=0.286
Question
Consider the set-up described in problem 22.32. Let x-bar be the average increase in charges observed in the sample. Let
mu be the average increase in charges that all of the card holders would have.
What are the null and alternate hypotheses for this situation?
Answer
Ho: mu=0 vs. Ha: mu<0
Ho: mu=0 vs. Ha: mu>0
Ho: mu>0 vs. Ha: mu=0
Ho: mu<0 vs. Ha: mu=0
Ho: x-bar=0 vs. Ha: x-bar<0
Ho: x-bar=0 vs. Ha: x-bar>0
Ho: x-bar>0 vs. Ha: x-bar=0
Ho: x-bar<0 vs. Ha: x-bar=0
Question
Consider testing Ho: p=0.2 against Ha: p<0.2.
With alpha=0.10 and a p-value of 0.075 we would...
Answer
Fail to reject the null hypothesis and conclude p=0.2
Fail to reject the null hypothesis and conclude p<0.2
Fail to reject the null hypothesis and conclude we don't have enough evidence to say p<0.2
Reject the null hypothesis and conclude p=0.2
Reject the null hypothesis and conclude p<0.2
Reject the null hypothesis and conclude we don't have enough evidence to say p<0.2
Homework 26
Question Consider the setting in problem 22.12. Let p be the proportion of all people with a temperature lower than 98.6. Let
p-hat be the proportion of people in your sample with a temperature lower than 98.6. The null and alternate hypotheses are:
Answer
Ho: p=0.5 vs. Ha: p<0.5
Ho: p=0.5 vs. Ha: p>0.5
Ho: p<0.5 vs. Ha: p=0.5
Ho: p>0.5 vs. Ha: p=0.5
Ho: p-hat=0.5 vs. Ha: p-hat<0.5
Ho: p-hat=0.5 vs. Ha: p-hat>0.5
Ho: p-hat<0.5 vs. Ha: p-hat=0.5
Ho: p-hat>0.5 vs. Ha: p-hat=0.5
Question If you decide to use a bigger alpha, then:
Answer
The null hypothesis will be rejected less often when it is true, and less often when it is false.
The null hypothesis will be rejected less often when it is true, and more often when it is false.
The null hypothesis will be rejected more often when it is true, and less often when it is false.
The null hypothesis will be rejected more often when it is true, and more often when it is false.
Question A researcher looking for evidence of extrasensory perception (ESP) tests 200 psychics independently using
alpha=0.05 in each case. The hypotheses are Ho: accuracy of that psychic is equal to random guessing and Ha: accuracy of
that psychic is better than random guessing. One of these suppopsed psychics gets a significant p-value of 0.01. The rest
have p-values greater than 0.05.
Answer
W ith a p-value of 0.01 that is less than or equal to alpha=0.05 we reject the null hypothesis and conclude that
we have evidence to say this psychic is able to predict better than chance.
With a p-value of 0.01 that is less than or equal to alpha=0.05 we fail to reject the null hypothesis and do not
have the evidence to conclude that the psychic can predict differently than guessing.
W ith 200 tests being done at alpha=0.05, we would actually expect to find