Statistics 311 Learning Objectives Data Collection and Surveys A1 Given a study identify population sample parameter sampling frame and statistic A2 Given a survey sample determine if the sample is a voluntary response sample or a convenience sample A3 Given a study recognize typical forms of biases such as potential undercoverage nonresponse and response bias A4 Given a study determine whether a SRS stratified random sample cluster sample or systematic sample was selected A5 Given a study s objective decide when to use a stratified random sample cluster sample systematic sample or SRS A6 Given a description of a study determine if it the study is a census or a sample survey Summarizing with Graphics B1 Given a set of raw data identify the individuals and the variables B2 Given a variable determine whether it is categorical or quantitative B3 List which graphical methods pie charts histograms etc are appropriate for categorical and for quantitative variables B4 Given a histogram stem plot or dot plot determine the number of individuals in a particular range B5 Given a set of raw data create a histogram dot plot or stemplot by hand or with appropriate software B6 Given a histogram dot plot or stemplot describe the distribution s shape skewed left skewed right symmetric or multimodal center and spread B7 Given a histogram dot plot or stemplot identify values that would be considered outliers B8 Given a graphical summary propose an explanation of the distribution of the data B9 Given a description of a variable predict what shape the histogram of that variable would take Summarizing with Numbers C1 Given a set of raw data calculate the principle summary statistics mean median quartiles inter quartile range variance standard deviation by hand or using appropriate software C2 Explain how the mean and median are related for different shapes of a distribution skewed left skewed right or symmetric C3 List the following characteristics of the standard deviation a The standard deviation must be greater than or equal to zero b When standard deviation is equal to zero there is no spread every number on the list is the same C4 Given a set of summary statistics mean median and standard deviation find the summary statistics of a data set that would result from a linear transformation of the original data A linear transformation means adding or subtracting the same value from each observation and or multiplying or dividing each observation by the same value C5 Given a histogram be able to determine the approximate location of the median and quartiles C6 Match given histograms dot plots or boxplots to given sets of appropriate summary statistics For example mean median standard deviation and quartiles C7 Explain the impact of outliers on summary statistics such as mean median and standard deviation C8 Given a set of raw data or five number summary create boxplot Given a boxplot determine the five number summary for that data C9 Given a boxplot determine if a distribution is skewed right or skewed left C10 Given side by side boxplots contrast key features of the groups represented by the boxplots The Normal Distribution D1 Explain that the normal distribution is a model for a bell shaped histogram D2 List the key characteristics of the normal distribution D3 Given a mean and standard deviation use the 68 95 99 7 rule to find the percentage of the normal distribution within one two or three standard deviations of the mean D4 Given a mean standard deviation and observed value x calculate the standardized value z score Describe the characteristics of a standard score D5 Given a z score use a normal table to find the corresponding probability D6 Given a mean and standard deviation find a specified percentile of the normal distribution e g Given a probability find the corresponding value of x Sampling Distributions E1 Describe the sampling distribution of a statistic and define the standard error of a statistic E2 Given a study describe the sampling distribution of x bar as specifically as possible This involves stating whether this distribution is at least approximately normal E3 Given a population standard deviation calculate the standard deviation of the sample mean x using the formula n E4 Given a population mean standard deviation sample size n and sample mean calculate the standardized value z score for a sample mean E6 Given a population proportion p calculate the standard deviation of the sample proportion p using the formula p 1 p n E7 Given a study describe the sampling distribution of the sample proportion p as specifically as possible This involves stating whether this distribution is at least approximately normal E8 Given a population proportion p sample size n and sample proportion p calculate the standardized value z score for a sample proportion Confidence Intervals F1 Calculate the standard error of the sample proportion p using the formula p 1 p n or the sample mean x using the formula s n F2 Given a study determine whether the study meets the conditions under which inferences on a population proportion may be performed For example requiring a simple random sample F3 Given a confidence level C determine the critical value z from the standard normal table needed to construct the confidence interval F4 Explain that confidence intervals are random quantities which vary from sample to sample and that they may miss the true population parameter Explain that the confidence level is that proportion of possible samples for which the confidence interval will capture the true parameter F5 Construct a confidence interval for a population proportion using the p 1 p formula p z n F6 Given a study interpret the result of a confidence interval in the context of the problem F7 Given a study determine whether the study meets the conditions under which inferences on a population mean may be performed For example requiring a simple random sample Also explain how inferences based on the t distribution are robust F8 Explain why we use the t distribution instead of the normal distribution when making inference the population mean F9 Given a sampling situation determine the appropriate degrees of freedom associated with the t distribution F10 Explain the differences and similarities between the normal and t distributions For example the t distribution is more variable but approaches normality as n increases F11 Given a confidence level C determine the critical value t from the t table needed to construct