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:

Revelation Therapies

Therapeutic approaches that emphasize the uncovering or discovery of truths or insights that can lead to emotional healing or psychological improvement.

Psychoanalytic Approach

A theory and method of psychological treatment developed by Sigmund Freud that emphasizes unconscious processes and childhood experiences in understanding and treating psychopathology.

Medical Degree

A qualification awarded to students who have successfully completed a course of study in medicine, qualifying them to work as a physician or surgeon.

Free Association

A psychoanalytic technique where patients are encouraged to verbalize any thoughts that come to mind without censorship.