Videocassette Recorder (VCR) Tapes Are Designed So That Users Can

question 96

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. $$\begin{array} { | c | c | c | c | c | c | } \hline { \text { Old-style tapes } } &&& { \text { New-technology tapes } } \\\hline 60 & 61 & 48 & 68 & 70 & 58 \\\hline 51 & 46 & 66 & 74 & 72 & 69 \\\hline 66 & 63 & 61 & 77 & 73 & 49 \\\hline 73 & 55 & 71 & 59 & 66 & 61 \\\hline 71 & 49 & 76 & 52 & 58 & 59 \\\hline 47 & 56 & 55 & 66 & 51 & 49 \\\hline 60 & 62 & 64 & 62 & 59 & 57 \\\hline 52 & 51 & 63 & 51 & 56 & 66 \\\hline 64 & 68 & 52 & 50 & 55 & 76 \\\hline 47 & 55 & 58 & 63 & 68 & 78 \\\hline\end{array}$$ Estimate with 90% confidence the proportion of unacceptable old tapes, and briefly describe what this interval estimate tells you.

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Definitions:

Fictional Finalism

A principle in Adlerian psychology proposing that an individual is motivated more by his or her expectations of the future than by past experiences.

Dominant Type

In personality theory, this refers to the primary or most influential trait or pattern within an individual's personality.

Avoiding Type

A personality style characterized by a tendency to avoid confrontation, risk, and stress.

Basic Style of Life

An Alfred Adler concept referring to an individual’s unique way of achieving personal goals and coping with the challenges of life.