Videocassette Recorder (VCR) Tapes Are Designed So That Users Can $\text { Old-style tapes }$

question 103

Essay

Videocassette recorder (VCR) tapes are designed so that users can repeatedly record new material over old material. However, after a number of re-recordings the tape begins to deteriorate. A VCR tape manufacturer is experimenting with a new technology, which hopefully will produce longer-lasting tapes. Thirty of the old-style tapes and 30 utilising the new technology were used in an experiment. The tapes were used to record and re-record programs until they began to deteriorate. The number of re-recordings is assumed to be normally distributed. It is generally accepted that the number of re-recordings should exceed 55. Any tapes that do not meet this criterion are considered to be unacceptable. The number of re-recordings were observed and shown in the accompanying table. $\text { Old-style tapes }$$\quad\quad\text { New-technology tapes }$
$\begin{array}{|l|l|l|l|l|l|}\hline 60\quad & 61 \quad& 48 \quad& 68\quad & 70\quad & 58 \quad\\\hline 51 & 46 & 66 & 74 & 72 & 69 \\\hline 66 & 63 & 61 & 77 & 73 & 49 \\\hline 73 & 55 & 71 & 59 & 66 & 61 \\\hline 71 & 49 & 76 & 52 & 58 & 59 \\\hline 47 & 56 & 55 & 66 & 51 & 49 \\\hline 60 & 62 & 64 & 62 & 59 & 57 \\\hline 52 & 51 & 63 & 51 & 56 & 66 \\\hline 64 & 68 & 52 & 50 & 55 & 76 \\\hline 47 & 55 & 58 & 63 & 68 & 78 \\\hline\end{array}$ Estimate with 90% confidence the ratio of the variances of the number of re-recordings of the two types of tape, and briefly describe what the interval estimate tells you.

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Definitions:

Narrow Spans of Control

A managerial structure in which a manager oversees a small number of subordinates, allowing for more direct supervision and communication.

Management Levels

The different layers of management in an organization, typically categorized into top-level (executives), middle-level (managers), and lower-level (supervisors or team leaders).

Environmental Uncertainty

The degree to which an organization lacks information about its external environment, making it difficult to predict future trends or events.

Systems Design

Refers to the process of defining the architecture, components, modules, interfaces, and data for a system to satisfy specified requirements.