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

question 21

Short Answer

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 difference in the proportions of unacceptable tapes between the old and new tapes.

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Definitions:

Book Value

The net value of an asset according to its balance sheet account balance, calculated as the original cost minus accumulated depreciation.

Variable Manufacturing Costs

Expenses that change in proportion to the amount of goods or services produced, including direct materials and labor.

Trading In

The act of submitting a used item as partial payment for another item, often seen in automotive and electronics purchases.

Salvage Value

The estimated residual value of an asset at the end of its useful life, often considered for depreciation calculations or when disposing of the asset.