Examples of df in the following topics:
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- The notation for the F distribution is F∼Fdf(num),df(denom) where df(num) = dfbetween and df(denom) = dfwithin
- The mean for the F distribution is $\mu =\frac{ df(num) }{df(denom)1 }$
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- where df = degrees of freedom depend on how chi-square is being used.
- (If you want to practice calculating chi-square probabilities then use df = n−1.
- For the χ2 distribution, the population mean is µ = df and the population standard deviation is $\sigma = \sqrt{2 \cdot df}$.
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- We revise the confidence interval formula slightly when using the t distribution: $\bar{x}\pm t^*_{df}SE$
- The value $t^*_{df}$is a cutoff we obtain based on the confidence level and the t distribution with df degrees of freedom.
- In our current example, we should use the t distribution with df = 19−1 = 18 degrees of freedom.
- Estimate the standard error of $t^*_{df}$ = 0.287 ppm using the data summaries in Exercise 5.20.
- Degrees of freedom: df = n−1 = 14.
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- When df > 90, the chi-square curve approximates the normal.
- For X∼$X^2_{1000}$ the mean, µ = df = 1000 and the standard deviation, σ =√(2·1000) = 44.7.
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- Since we can assume that there is a cylindrical symmetry in the blood vessel, we first consider the volume of blood passing through a ring with inner radius $r$ and outer radius $r+dr$ per unit time ($dF$):
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- The degrees of freedom ($df$) is a somewhat complicated calculation.
- The $df$s are not always a whole number.
- The test statistic calculated above is approximated by the student's-$t$ distribution with $df$s as follows:
- Distribution for the test: Use $t_{df}$ where $df$ is calculated using the $df$ formula for independent groups, two population means.
- Using a calculator, $df$ is approximately 18.8462.
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- Find the following: 2.1 df (num) = 2.2 df (denom) =