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Chapter 6. Probability
Chapter 7: Probability and Samples: The…
Chapter 6. Probability
Chapter 7: Probability and Samples: The Distribution of Sample Means
Chapter 8: Introduction to Hypothesis Testing
What is random sampling? A random sample requires that each individual in the population has an equal chance of being selected. A sample obtained by this process is called a simple random sample.
What is sampling with replacement? A sampling technique that returns the current selection to the population before the next selection is made. A required part of random sampling.
Unit Normal Table: A table listing proportions corresponding to each z-score location in a normal distribution.
What is a Binomial Distribution? A binomial distribution is a scale that shows the probability associated with each value of X.
Using the notation presented here, the binomial distribution shows the probability associated with each value of X from to .
Chapter 6: PROBABILITY: For a situation in which several different outcomes are possible, the probability for any specific outcome is defined as a fraction or a proportion of all the possible outcomes. If Adna rolls 2 dice, the probability of her rolling a sum of seven is higher than the other sums.
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Sampling error is the natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter.
Futhermore, if you take two separate samples from the same population, the samples will be different. They will contain different individuals, they will have different scores, and they will have different sample means.
Central Limit Theorem: A mathematical theorem that specifies the characteristics of the distribution of sample means. According to the central limit theorem, the 3 parameters of the distribution of sample means are shape, central tendency, and variability.
SHAPE: The distribution of sample means is normal if either one of the following two conditions is satisfied: (1)The population from which the samples are selected is normal. (2)The size of the samples is relatively large (around or more).
CENTRAL TENDENCY: The mean of the distribution of sample means is identical to the mean of the population from which the samples are selected. The mean of the distribution of sample means is called the expected value of M.
VARIABILITY: The standard deviation of the distribution of sample means is called the standard error of M and is defined by the formula
LAW OF LARGE NUMBERS: The law of large numbers states that the larger the sample size (n), the more probable it is that the sample mean will be close to the population mean. :
In general, as the sample size increases, the error between the sample mean and the population mean should decrease.
The alpha level for a hypothesis test is the probability that the test will lead to a Type I error. That is, the alpha level determines the probability of obtaining sample data in the critical region even though the null hypothesis is true.
Types of Statistical Errors : Type 1 and Type 2
A Type I error occurs when a researcher rejects a null hypothesis that is actually true. In a typical research situation, a Type I error means the researcher concludes that a treatment does have an effect when in fact it has no effect.
A Type II error occurs when a researcher fails to reject a null hypothesis that is really false. In a typical research situation, a Type II error means that the hypothesis test has failed to detect a real treatment effect.
Chapter 8: HYPOTHESIS TESTING is a statistical method that uses sample data to evaluate a hypothesis about a population.
A result of a hypothesis testing is said to be significant or statistically significant if it is very unlikely to occur when the null hypothesis is true. That is, the result is sufficient to reject the null hypothesis. Thus, a treatment has a significant effect if the decision from the hypothesis test is to reject .
The critical region is composed of the extreme sample values that are very unlikely (as defined by the alpha level) to be obtained if the null hypothesis is true. The boundaries for the critical region are determined by the alpha level. If sample data fall in the critical region, the null hypothesis is [rejected.]
Directional Testing: A directional test is a hypothesis test that includes a directional prediction in the statement of the hypotheses and places the critical region entirely in one tail of the distribution.
Cohen's d: A standard measure of effect size computed by dividing the sample mean difference by the sample standard deviation.