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

question 34

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. $$\begin{array} { | c | c | c | c | c | c | } \hline { \text { Old-style tapes } } &&& { \text { New-technology tapes } } \\\hline 60 & 61 & 48 & 68 & 70 & 58 \\\hline 51 & 46 & 66 & 74 & 72 & 69 \\\hline 66 & 63 & 61 & 77 & 73 & 49 \\\hline 73 & 55 & 71 & 59 & 66 & 61 \\\hline 71 & 49 & 76 & 52 & 58 & 59 \\\hline 47 & 56 & 55 & 66 & 51 & 49 \\\hline 60 & 62 & 64 & 62 & 59 & 57 \\\hline 52 & 51 & 63 & 51 & 56 & 66 \\\hline 64 & 68 & 52 & 50 & 55 & 76 \\\hline 47 & 55 & 58 & 63 & 68 & 78 \\\hline\end{array}$$ a. Do the data allow us to infer at the 10% significance level that the new-technology tapes are superior to the old-style tapes in terms of the number of unacceptable tapes?
b. Find the p-value of the test in a. and explain how to use it to test the hypotheses.

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Definitions:

Lazarus Theory

A psychological theory that suggests that the experience of stress is a result of an interaction between an individual's perception of a stressor and their ability to handle or cope with the stressor.

Physiological Reaction

A bodily response to an internal or external stimulus, involving complex biological processes and mechanisms.

James-Lange Theory

A theory of emotion proposing that emotions result from the perception of bodily reactions to stimuli, suggesting that we feel sad because we cry, angry because we strike.

Intrinsic Motives

Internal drives that inspire behavior based on internal rewards, satisfaction, or personal fulfillment.