Statistical inference draws conclusions about a population or process based on sample data. This chapter will only consider scenarios of inference about the mean with the standard deviation given. In this setting we can ask questions like: Purpose of statistical inference is to draw conclusion from data. Probability allows us to take chance variation into account. 20 were given the drug 60% had improvement. 20 were given the placebo 40% had improvement. Due to probability calculations a difference this large or larger between the results in the two group would occur one time in five simply because of chance variation. Confidence interval used for estimating the value of a population parameter. Tests of significance assess the evidence for a claim. Both types of inferences are based on sampling distributions of statistics. Probability models are most secure, and inference is most reliable when the data are produced by a properly randomized design.