CHAPTER 13: t TEST FOR ONE SAMPLE Key Terms Sampling distribution of t the distribution of t values that would be obtained if a value of t was calculated for each sample mean for all possible random sample of a given size from some population. Sample standard deviation the version of the sample standard deviation, with n-l in its denominator, which is used in statistical inference to estimate the unknown population. Estimated standard error of the mean i The version of the standard error of the mean that is used whenever the unknown population standard deviation must be estimated. t ratio 7 A replacement for the 2 ratio whenever the unknown population standard deviation must be estimated. Degree of freedom 7 the number of values free to vary, given one or more mathematical restrictions on a sample of observed values used to estimate some unknown population characteristic. Text Review The sampling distribution of t was discovered by (1) . In reality, there is a family of t distribution, each associated with a number referred to as (2) In the present case, the number of degrees of freedom (dt) always equals (3) All t distributions are similar to z distributions in that they are symmetrical, unimodal, and bell shaped. The biggest difference betweent and z distributions 1s the (4) of the t distribution. Tables for t distributions contain only the values that correspond to the common levels of signicance. The tvalues listed in the table are (5) and originate from the (6) half of the distribution. The symmetry allows the critical t values for the lower half of the distribution to be obtained by simply placing a negative sign in 'ont of any table entry. The t distribution has greater variability than 2 distribution. This increased variability arises from the estimated standard error of the mean and the chance differences that could occur in the estimates. The extra variability also explains the inated tails of the curve in the t distribution. Because of this extra variability, one could expect actual critical t values to be (7) than critical 2