Note that this table requires the use of degrees of freedom (dof or df or v) which are calculated as the sample size minus 1. The degrees of freedom are shown in Figure 2.22 in the first column to the left (v) and the level of significance is the first row in the same figure. The level of significance equates to the area under the curve and hence the letter A is used in the first row in Figure 2.22.
2.10 The =tinv() function To calculate the Critical-t value used in the hypothesis testing example above the Excel function =tinv() is used. =tinv() is used to find the t-value as a function of the probability and the degrees of freedom. The format of the function is =tinv(probability, df) Where probability=the probability associated with the two-tailed t test by default. df = the degrees of freedom which is equal to n-1 The formula in cell B11 in Figure 2.23 uses =tinv() We can determine the theoretical (Critical-t) value at a specified level of significance, e.g. for a significance level of 5% the theoretical Critical-t value for the above example is 1.73. This was produced by entering =tinv(2*B5,B3-1). As the Calc-t value 1.63 is less than the Critical-t value 1.73 the Null Hypothesis cannot be rejected. The rule is….if the absolute value of Calc-t >Critical-t then reject. Note that the t-statistic has been typically used for small samples i.e. samples containing less than 30 data points. However, for large samples (i.e. with 30 or more data points) the t-distribution and the normal distribution are almost identical. Thus the t-distribution is sometimes used across the whole range of values.
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