Term
| _____is a measure of the likelihood of a particular outcome or a result. It can be estimated by the proportion of times an outcome occurs in a ______. |
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Definition
| probability; large number of trials |
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Term
| The_____states that the number of times an experiment is repeated is increased, the ratio of the number of successful occurences to the number of trials will tend to approach the probability of the event. |
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Definition
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Term
| What is the first step when calculating probability? |
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Definition
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Term
| The _____of an experiment is the complete set of possible outcomes. |
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Definition
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Term
| What is the sample space for one coin toss? |
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Definition
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Term
| What is the sample space for one die toss? |
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Definition
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Term
| If you are rolling a die, let A denote the event of 'rolling an even number'. Which outcomes are in event A? |
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Definition
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Term
| We define the _______, denoted P(A), a the likelihood of the event occuring. And the idea that, with any roll of a die, we could roll 1, 2, 3, 4, 5 or 6 is called _____. |
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Definition
| probability of an event A; randomness |
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Term
| What is the sample space when you throw a fair coin twice? |
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Definition
| Heads, Heads; Tails, Tails; Heads, Tails; Tails, Heads |
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Term
| What outcomes are included in the event getting at least one head? (throwing a fair coin twice) |
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Definition
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Term
| Counting up the number of equally likely outcomes in an event, and dividing by the total number of equally likely outcomes in the sample sapce allow you to find a _____ |
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Definition
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Term
| What is another name for classical probability? |
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Definition
| relative frequency probability |
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Term
| HOw do you find the classical probability? |
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Definition
| divide the number of ways an event can occur by the total number of possible otucomes |
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Term
| A_____is a a probability that is based on subjective judgment and personal opinion. |
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Definition
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Term
| What are the two properties of probability? |
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Definition
| the probability of any event must be between 0 and 1; the total of all the individual probabilities equals one |
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Term
| What does it mean if the probability is equal to zero? |
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Definition
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Term
| What does it mean if the probability is equal to 1? |
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Definition
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Term
| If the probability is closer to one, is it more likely or less likely to happen? |
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Definition
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Term
| The ____of an event A contains all outcomes in the sample space that are not in event A. |
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Definition
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Term
| What is the formula for finding the complement of an event? |
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Definition
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Term
| According to the National Gambling Impact Study Commission, 52% of Americans have played state lotteries. What is the probability that a randomly selected American has not played a state lottery? |
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Definition
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Term
| ____are formed by combining two or more events. |
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Definition
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Term
| On one roll of a die, what is the probability of rolling an even number AND rolling a number higher than 4? |
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Definition
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Term
| On one roll of a die, what is the probability of rolling an even number OR rolling a number higher than 4? |
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Definition
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Term
| A_____is the probability of one event happening given that a different event has already occured. |
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Definition
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Term
| If you roll a die, and you know you have rolled an even number, what is the probability that you have rolled a 6? |
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Definition
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Term
| conditional probability---knowing a conditon...given that |
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Definition
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Term
| A and B are said to be ______if knowing that A happens doesnt cahnge the probability that B happens. |
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Definition
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Term
| A and B are ____if knowing that A happens does change or affect the probability that B happens. |
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Definition
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Term
| A random variable is a varaible that takes on a particular ____based on each possible outcome of an experiment |
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Definition
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Term
| What are the two types of random variables? |
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Definition
| discrete random variable; continuous random variable |
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Term
| A _____is a random variable that can only assume a countable number of distinct possible values. |
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Definition
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Term
| What is an example of a discrete random variable? |
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Definition
| the number of heads in three flips of a coin |
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Term
| A______can assume an uncountable, infinite number of possible values. Just as before, these values are on an interval. |
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Definition
| continuous random variable |
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Term
| What is an example of a continuous random variable? |
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Definition
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Term
| A_____of a discrete random variable is a table, graph, or mathematical equation that provides the possible values of the random variable and their corresponding probailities. |
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Definition
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Term
| What are the requiremtns of a probability distribution? in other words, in order to be a valid probability distribution what two things must be true? |
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Definition
| for each x, the probability P(X) falls between 0 and 1; the sum of the probabilities for all the possible x values =1 |
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Term
| The mean of a probability distribution for a discrete random variable is given by the formula.... |
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Definition
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Term
| When calculating the mean of a probability distribution, you are really calculating an average or mean outcome using all the possible outcomes and their corresponding probabilities. We call this a ______. |
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Definition
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Term
| The mean of a random variable is the long-run average outcome of the experiment. In this sense, as the number of trials of the experiment increases, what happens to the average result of the experiment? |
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Definition
| it gets closer to the mean of the random variable |
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Term
| The mean of a random variable X is often called the _____, denoted E(X). |
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Definition
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Term
| There are three envelopes in a game--one contains $45 and the other two contain nothing. For the players how many different outcomes to the game are there? What is the probability for each outcome? What is the expected value for this game? |
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Definition
| two; 2/3 for 0 and 1/3 for 45; $15 is the expected value |
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Term
| When we have data that is continuous, which can include numerous decimal places, the graph of our data transforms from a _____to a a_____. |
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Definition
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Term
| To find probabilities for continuous random vraibles, we must find ______. |
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Definition
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Term
| A _____random variable has possible values that form an interval. Each interval has probability between 0 and 1, and the probability is the area under the curve in that interval. |
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Definition
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Term
| The interval containing all possible values has probability equal to 1, so the total area under the curve is equal to ____. |
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Definition
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Term
| What is the empirical rule? |
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Definition
| 68 % of the area under the normal curve is within one standard deviation of the mean; 95% of the area under the normal curve is within two standard deviations of the mean; 99.7 % of the area under the normal curve is within three standard deviations of the mean |
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Term
| A standard normal distribution has a mean of ___and a standard deviation of ___. |
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Definition
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Term
| What are the two ways to find probability? |
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Definition
| by putting in the actual mean and standard deviaiton and finding the probability associated with the value; by putting in mean=0 and standard deviaiton=1, converting your value into a z-score, and finding the probability associated with that z-score |
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Term
| Wehn a question asks for number of standard deviations, you are looking for ____, which have a mean of ____and a standard deviation of ___. |
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Definition
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Term
| When you are looking at an average instead of an individual, you need to use _____ |
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Definition
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Term
| A _____is the name given to a distribution for a sample statistic, such as a sample mean. |
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Definition
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Term
| The two sampling distributions we discuss are the sampling distribution of the _____, denoted as ____. And the sampling distribution of the _____, denoted as ____. |
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Definition
| sample mean--x bar; and sample proportion---p hat |
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Term
| If you asked a class how many siblings they had and figured out the average number of siblings for the whole class, is this a population mean or a sample mean? |
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Definition
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Term
| If you took a sample of ten people in a class and figured out the average number of siblings they had, then you would have a ____ |
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Definition
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Term
| If you are interested in seeing what the distribution of all the possible sample means would look like then that distribution is what you call the _____. |
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Definition
| sampling distribution of the sample mean |
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Term
| What is the mean or the overall average of all the possible sample means? |
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Definition
| on average, sample mean=population mean |
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Term
| What is the standard deviation, or in other words, the spread of the values for all the possible sample means? |
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Definition
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Term
| When we are talking about the spread, or standard deviation, of a sampling distribution, we call it the _____. |
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Definition
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Term
| The standard error is a type of standard deviation, but what does it measure? |
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Definition
| the spread a sample statistic like the sample mean; it just places a value on the spread of all the possible sample mean values |
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Term
| When we are talking about the sampling distribution of the sample mean, what are we referring to? |
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Definition
| the standard error; sd/sqrt (n) |
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Term
| For the most part, the sample means are going to average out _____the mean. |
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Definition
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Term
| Which is bigger, the standard deviaiton or the standard error? |
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Definition
| the standard error or spread is not going to be as big as the standard deviation |
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Term
| The ______is an important rule in statistics that tells us when the sampling distribution of the sample mean will be normally distributed. |
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Definition
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Term
| What does the central limit theorem state? (2 things) |
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Definition
| if the population we are sampling from is normally distributed then the sampling distribution of the sample mean is normally distributed, regardless of sample size; if we are using a large enough sample size (usually we say n greater than 30), then the sampling distribution of the sample mean is approximately normal regardless of the distribution of the population |
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Term
| How do you check to see if the sampling distribution of the sample mean is normally distributed? |
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Definition
| check to see if the population we are sampling from is normal OR if we are using n>30 |
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Term
| When we want to find probabilities/areas under the curve involving sample means, we will still put in ____for the mean in stat crunch, but we will now put in ____for the standard deviation. other than that, everything else will be the same. |
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Definition
| mu--population mean; sd/sqrt (n) |
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Term
| We use this new standard deviation (called the _____) because? |
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Definition
| standard error because sample means are not as spread out as much as indivudal data values, so the new standard deviation is sd/sqrt(n) rather than just the standard deviation |
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Term
| Suppose a single value is selected from a normal population with mean=5 and standard deviation=1. Are you looking for x or x bar? Why? |
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Definition
| x because it asks for a single value |
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Term
| Now suppose a sample of size 25 is selected from this population. Let's use statcrunch to find the probability that the sample mean for these 25 values is greater than 5.5. Are you lookng for x or x bar? |
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Definition
| x bar ebcause it asks for sample mean |
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Term
| Read all the questions carefully, make sure you know if it is asking for sample mean or individual value because that will determine your standard deviation |
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Definition
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Term
| The _____is the entire distribution from which we take the sample. The ____is the distribution of the sample data for each given sample. The ______is the probability distribution of a sample statistic, such as a sample mean. It is a distribution of all the possible values for the sample statistic. |
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Definition
| population distribution; sample; sampling distribution |
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Term
| _____measures the spread of data values. |
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Definition
| sample standard deviation |
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Term
| _____is a type of standard deviation that measures the spread of the possible sample statistic values. For example, ____measures how spread out the possible sample means are from different samples. |
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Definition
| standard error; standard error |
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Term
| WE use the letter ____to represent the population proportion. |
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Definition
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Term
| Let's say you figured out the proportion of women in an entire class, you have found the _____. |
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Definition
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Term
| Let's say you took a sample of ten people out of the class and figured out the proportion of women, you have now calculated the ______. |
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Definition
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Term
| What is the notation for sample proportion? |
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Definition
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Term
| When finding the sampling distribution of the sample proportion, the mean is ___. How would you find the standard deviation or standard error? |
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Definition
| mean=p. sd=sqrt[p(1-p)/n] |
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Term
| The sampling distribution of p hat will be approximately normal if ____is large. |
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Definition
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Term
| What is the criteria for what represents a large enough sample size? |
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Definition
| np> or equal 15 AND n(1-p)>or equal 15; BOTH CONDITIONS MUST BE MET |
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Term
| when you are given information about a sample and population proportion what shoudl you do first? |
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Definition
| first check to see if it's normal ---greater than 15 in BOTH categories; now find mean and standard deviation |
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