TABLE OF CONTENTS Approximately 95% of the area under the standard normal curve is between z = ? 1.96 and z = + 1.96. This interval is called 95% confidence interval for the population mean ?. Here, the word population refers to a particular situation where our estimates are based on, and the word sample implies a small selection from that population. For example, population may refer to a group of students passing a certain examination, and a sample may be one or more students from this population.
When the sample size is less than 30, the Student's t-distribution [*] or simply t-distribution is used instead of the standard normal distribution. The t-distribution is actually a family of probability distributions, and each separate t-distribution is determined by a parameter called the degrees of freedom, which we will denote as df. If n is the sample size for n < 30, then the degrees of freedom can be computed from
The t-distribution curves, like the standard normal distribution curve, are centered at zero. Thus, the mean is zero, that is,
The variance of each t-distribution depends upon the value of df. It is found from
Figure 11.17 shows the t-distribution for df = 1, df = 3, and df = 20 where we observe that, for higher values of df, this...
