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

question 98

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 }$
$\begin{array}{|l|l|l|l|l|l|}\hline 60\quad & 61 \quad& 48 \quad& 68\quad & 70\quad & 58 \quad\\\hline 51 & 46 & 66 & 74 & 72 & 69 \\\hline 66 & 63 & 61 & 77 & 73 & 49 \\\hline 73 & 55 & 71 & 59 & 66 & 61 \\\hline 71 & 49 & 76 & 52 & 58 & 59 \\\hline 47 & 56 & 55 & 66 & 51 & 49 \\\hline 60 & 62 & 64 & 62 & 59 & 57 \\\hline 52 & 51 & 63 & 51 & 56 & 66 \\\hline 64 & 68 & 52 & 50 & 55 & 76 \\\hline 47 & 55 & 58 & 63 & 68 & 78 \\\hline\end{array}$ Can we conclude at the 10% significance level that the mean number of re-recordings of the new tapes is at least 55?

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Definitions:

Adapt

The process of making changes or adjustments to accommodate new conditions or environments.

Richest Mode

The communication method that conveys the most information, including verbal and nonverbal cues, to facilitate understanding.

Communication

The process of exchanging information, ideas, or feelings between individuals or groups, often through speaking, writing, or using some other medium.

Specify the Age

To clearly state or identify the number of years someone or something has existed.