Suppose That a Random Sample of 150 Observations Was Drawn

question 52

Essay

Suppose that a random sample of 150 observations was drawn from a population. After calculating the mean and standard deviation, each observation was standardised and the number of observations in each of the intervals below was counted. Can we infer at the 5% significance level that the data were drawn from a normal population? $$\begin{array} { | c | c | } \hline \text { Intervals } & \text { Frequency } \\\hline Z \leq - 1.5 & 15 \\\hline - 1.5 < Z \leq - 0.5 & 32 \\\hline - 0.5 \leq Z \leq 0.5 & 65 \\\hline 0.5 < Z \leq 1.5 & 25 \\\hline Z > 1.5 & 13 \\\hline\end{array}$$

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Definitions:

Spur Gears

Cylindrical gears with teeth projecting radially and having edges parallel to the axis, used to transmit motion between parallel shafts in machinery.

Pinion

A small gear that engages with a larger gear or rack, often used to convert rotational motion to linear motion or vice versa.

Mechanical Advantage

The factor by which a mechanism multiplies the force put into it, enabling the lifting or moving of heavier loads with less effort.

Pitch Diameters

The effective diameter of a screw thread, halfway between the crests and roots, used in measuring and specifying thread sizes.