The table below provides a list of study questions (P, Q, R) and statistical tests (i, ii, iii).
Which one of the following options correctly matches the study question to the most appropriate statistical test?
The percent Fe content of a random sample consisting of five observations is shown:
If the mean grade of the stockpile is estimated using the above data, the standard error of the mean grade, in %, is _______ (rounded off to 3 decimal places).
For the following ten angle observations, the standard error of the mean angle is given as 2cm arcsecond (rounded off to 2 decimal places).
25$^\circ$40'12'' | 25$^\circ$40'14'' | 25$^\circ$40'16'' | 25$^\circ$40'18'' | 25$^\circ$40'09'' |
25$^\circ$40'15'' | 25$^\circ$40'10'' | 25$^\circ$40'13'' | 25$^\circ$40'15'' | 25$^\circ$40'18'' |
The residual error in a measurement comprises a bias of \( +0.08 \, {m} \) and a random component given by the following density function: \[ f(x) = \frac{1}{0.15 \sqrt{2\pi}} \exp\left( -\frac{x^2}{2 \cdot (0.15)^2} \right) \] For this system, the mean square error (MSE) is __________ m (rounded off to 2 decimal places).
The table lists the top 5 nations according to the number of gold medals won in a tournament; also included are the number of silver and the bronze medals won by them. Based only on the data provided in the table, which one of the following statements is INCORRECT?
Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction.
After the 1st round, the 4th student behind P leaves the game.
After the 2nd round, the 5th student behind Q leaves the game.
After the 3rd round, the 3rd student behind V leaves the game.
After the 4th round, the 4th student behind U leaves the game.
Who all are left in the game after the 4th round?
A stick of length one meter is broken at two locations at distances of \( b_1 \) and \( b_2 \) from the origin (0), as shown in the figure. Note that \( 0<b_1<b_2<1 \). Which one of the following is NOT a necessary condition for forming a triangle using the three pieces?
Note: All lengths are in meter. The figure shown is representative.