When comparing t-curves of 12 and 20 degrees of freedom in terms of their resemblance to the standard normal curve, the latter has a close semblance. In both cases, the studentized version of mean X follows the t distribution. This is because the degrees of freedom increases with an increase with sample size. In these cases, the sample sizes are 13 and 21 respectively since the t distribution formula is (n-1). Therefore, taking into account that the t-curve and the standard normal curve are symmetric, zero, and bell-shaped, the t-curve with 20 degrees of freedom becomes a close fit. The only difference exists in the nature of spreading whereby the t curve is more spread than the standard normal curve.
The studentized t-curve version is standardized in the unknown populations. In other words, the variability in all possible studentized deviation values for a fixed sample size decreases as the sample size increases. So the standard normal curve assumes an infinite population or sample. The more degrees of freedom in t-distribution, the closer to the normal distribution. Essentially, as the degree of freedom increases, the t-distribution starts to resemble the normal distribution more. Therefore, the t curve with a degree of freedom 20 would resemble the normal curve more. The normal distribution has generally more scores in the focal point of the dispersion and the t distribution has moderately more in the tails. The t distribution is along these lines leptokurtic. it moves toward the normal distribution as the degrees of freedom increment.
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In conclusion, the degrees of freedom determine the t distribution. These are independent observations of set data. The level of the distribution inside standard deviations of the mean is not exactly for the normal distribution. Thus the semblance between the 20 degrees t-curve with the normal curve than is the case with the 12 degrees t-curve.
