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

question 62

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 population variance of the number of re-recordings of the new tape.

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Definitions:

Aggregate Demand Curve

The aggregate demand curve represents the total quantity of all goods and services demanded by the economy at different price levels.

Aggregate Supply Curve

A graphical representation showing the relationship between the total production of goods and services in an economy and the overall price level.

Price Index

An average that measures the change in prices paid by consumers for goods and services over time, indicating inflation or deflation.

GDP

Gross Domestic Product, a measure of the economic performance of a country, indicating the total value of all goods and services produced over a specific time period.