Unit 4
Define Simulation
The imitation of chance behavior, based on a model that accurately reflects the situation (Book definition)
Continuous variables
Result from measuring something
If the equation =
np10 or n(1-p)10
It is approximately normal
m=np
Mean for binomial distributions
What is the purpose of reducing variability when collecting data?
To increase accuracy
Describe an event
An event is any collection of outcomes from some chance process (Book definition)
If knowing the value of X does not help us predict the value of Y, then X and Y are...
independent random variables.
Central limit theorem (CLT)
as sample size increases, the distribution of sample means approaches a normal distribution —regardless of the population's original distribution shape
Square root: [np(1-p)]
Standard deviation for binomials
The probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0.40. Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey.
Is Avery interpreting the probability correctly?
A.) Yes, because participants in the survey are selected at random
B.) Yes, because 2 out of 5 is equal to 40%.
C.) No, because 0.40 represents probability in the long run over many visits to the site.
D.)No, because there could be voluntary response bias.
C.) No, because 0.40 represents probability in the long run over many visits to the site.
If a fair coin is tossed five times and the outcomes are TTTTT, then the probability that tails appears on the next toss is
a.) 0.5
b.) less than 0.5
c.) greater than 0.5
d.) 1
a.) 0.5
Discrete random variable
Results from counting something
Why might a researcher decide to expand the population of people being tested/surveyed when collecting data?
To reduce variability
P(x=k)=n(kpk (1-p)n-k
Binomial formula
Following a recent dramatic drop of 500 points in the Dow Jones Industrial Average, a poll conducted for the Associated Press found that 92% of those polled said that a year from now their family financial situation will be as good as it is today or better. Which of the following terms describes the number 92%?
A.) Population
B.) Statistic
C.) Parameter
D.) Variable
B.) Statistic
True or false: The probability of any event is a number between 0 and 1.
True
True or false: Adding or subtracting a constant affects the distribution of a quantitative variable and the probability distribution of a random variable in exactly the same way.
True
Define Variability
How spread out the sampling distribution is
Z= x - mean / standard deviation
Z-score Formula
Selling eggs that are contaminated with salmonella can cause food poisoning in consumers. A large egg producer randomly selects 200 eggs from all eggs shipped in one day. The laboratory reports that 9 of these eggs had salmonella contamination. Identify the population, parameter, and the sample.
Population: All eggs shipped in one day
Parameter:Proportion of eggs shipped that day with salmonella
Sample: 200 eggs examined
You read in a book about bridge that the probability that each of the four players is dealt exactly 1 ace is approximately 0.11. This means that:
a.) in every 100 bridge deals, each player has 1 ace exactly 11 times.
b.) in 1 million bridge deals, the number of deals on which each player has 1 ace will be exactly 110,000.
c.) in a very large number of bridge deals, the percent of deals on which each player has 1 ace will be very close to 11%.
d.) in a very large number of bridge deals, the average number of aces in a hand will be very close to 0.11.
c.) In a very large number of bridge deals, the percent of deals on which each player has 1 ace will be very close to 11%.
Describe the relationship between randomness and probability
Probability describes the likelihood of outcomes in random processes
What is an unbiased estimator
Center equals the true value
Meanx = np
Geometric distribution formula
Value: 1, 2, 3, 4, 5
Probability: 0.1, 0.2, 0.3, 0.3, ?
What is the probability of value 5?
P: 0.1