Question

The coefficient of variation (CV) for a random sample $Y_1, ..., Y_n$ is defined by $\qquad CV = \frac{S}{\bar{Y}}$, where $S$ is the sample standard deviation and $\bar{Y}$ is the sample mean. CV measures the amount of variation as a proportion of the sample mean. Suppose each $Y_i \sim N(0, \sigma^2)$ for $i = 1, ..., 10$. (a) By using $F_{1, \nu} = t_{\nu}^2$, find the distribution of $10\bar{Y}^2 / S^2$ in terms of the F-distribution. (b) Find the distribution of $S^2 / (10\bar{Y}^2)$. (c) Using statistical tables, find the number $c$ such that $\qquad Pr\left\{-c \le \frac{S}{\bar{Y}} \le c\right\} = .95$.

          The coefficient of variation (CV) for a random sample $Y_1, ..., Y_n$ is defined by
$\qquad CV = \frac{S}{\bar{Y}}$,
where $S$ is the sample standard deviation and $\bar{Y}$ is the sample mean. CV measures the amount of
variation as a proportion of the sample mean. Suppose each $Y_i \sim N(0, \sigma^2)$ for $i = 1, ..., 10$.
(a) By using $F_{1, \nu} = t_{\nu}^2$, find the distribution of $10\bar{Y}^2 / S^2$ in terms of the F-distribution.
(b) Find the distribution of $S^2 / (10\bar{Y}^2)$.
(c) Using statistical tables, find the number $c$ such that
$\qquad Pr\left\{-c \le \frac{S}{\bar{Y}} \le c\right\} = .95$.

$The coefficient of variation (CV) for a random sample Y1, ..., Yn is defined by CV = (S)/(Y̅), where S is the sample standard deviation and Y̅ is the sample mean. CV measures the amount of variation as a proportion of the sample mean. Suppose each Yi ∼ N(0, σ^2) for i = 1, ..., 10. (a) By using F1, ν = tν^2, find the distribution of 10Y̅^2 / S^2 in terms of the F-distribution. (b) Find the distribution of S^2 / (10Y̅^2). (c) Using statistical tables, find the number c such that Pr{-c ≤(S)/(Y̅)≤ c} = .95.$

Added by Jose Angel A.

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