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Chapter 5

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Psychology 1000
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Bio 2244B Textbook Notes Chapter 5 51 52 53 54 55 56February th8 201251 OverviewDefinitionsNormal distribution if a continuous random variable has a distribution with a graph that is symmetric and bellshaped and can be described by the following equation 21x2ey2Uniform distribution if a continuous random variable has vales that spread evenly over the range of possibilities The graph of a uniform distribution results in a rectangular shapeDensity curve a graph of a continuous probability distribution It must satisfy the following properties1The total area under the curve must equal 12Every point on the curve must have a vertical height that is 0 or greater that is the curve cannot fall below the xaxisoBecause the total area under the density curve is equal to 1 there is a correspondence between area and probabilityStandard normal distribution a normal probability distribution that has a mean of 0 and a standard deviation of 1 and the total area under its density curve is equal to 1Zscore distance along the horizontal scale of the standard normal distribution see image rightArea region under the curve53 Applications of Normal DistributionsIf we convert values to standard scores using the following formula then procedures for working with all normal distributions are the same as those for the standard normal xzdistribution 54 Sampling Distributions and EstimatorsWhy sample with replacement 1When selecting a relatively small sample from a large population it makes no significant difference whether we sample with replacement or without replacement2Sampling with replacement results in independent events that are unaffected by previous outcomes and independent events are easier to analyze and they result in simpler formulasSampling distribution of the mean the probability distribution of sample means with all samples having the same sample size n In general the sampling distribution of any statistic is the probability distribution of that statisticSampling variability the value of a statistic such as the sample mean x depends on the particular values included in the sample and it generally varies from sample to sampleSampling distribution of the proportion the probability distribution of sample proportions with all samples having the same sample size nProperties of the distribution of sample proportionsoSample proportions tend to target the value of the population proportion oUnder certain conditions the distribution of sample proportions approximates a normal distribution
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