## Degrees of freedom and t tables

Table 2-1 is an abbreviated t score table that shows the values of t corresponding to different areas under the normal distribution for various sample sizes. Tables of t values do not show sample size (n) directly; instead, they express sample size in terms of degrees of freedom (df). For the purposes of USMLE, degrees of freedom (df) can be defined as simply equal to n — 1. Therefore, ro determine the value of t (such that 95% of the population of t-statistics based on a sample size of 15 lies between — t and +t), one would look in the table for the appropriate value of t for df = 14 (14 being equal to n — 1); this is sometimes written as t,4. Table 2-1 shows that this value is 2.145.

As n becomes larger (100 or more), the values of t are very close to the corresponding values of z- As the middle column shows, for a df of 100, 95% of the distribution falls within t = ± 1.984; while for a df of this figure is 1.96, which is the same figure for z (see Table 1-3). In general, the value of t that divides the central 95% of the distribution from the remaining 5% is in the region of 2, just as it is for (One- and two-tailed tests are discussed in Chapter 3 in the section on Directional Hypotheses).

As an example of the use of t scores, we can repear the earlier task of estimating (with 95% confidence) the true mean resting heart rate of a large population, basing the estimate on a random sample of people drawn from this population. This time we will not make the unrealistic assumption that the standard error is known.

As before, a random sample of 15 people is drawn, and it is found that their mean heart rate (X) is 74 beats/min. Assuming that the standard deviation of this sample is 8.2, the estimated standard error, can be calculated as follows:

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Your heart pumps blood throughout your body using a network of tubing called arteries and capillaries which return the blood back to your heart via your veins. Blood pressure is the force of the blood pushing against the walls of your arteries as your heart beats.Learn more...

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