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:

Loud Music

High-volume sound produced by musical instruments or audio equipment that can either be enjoyable or cause discomfort depending on the context and individual preferences.

Soft Music

A genre or style of music characterized by its gentle, soothing, and tranquil qualities, often used for relaxation and stress relief.

Extraverts

Characterized by their energetic, enthusiastic, and sociable behavior, often seeking stimulation and company in their surroundings.

Introverts

Individuals who tend to be more inward-turning, focusing on internal thoughts, feelings, and moods rather than seeking out external stimulation.