t=3953.28 and t²=244,557.00
a. Constructing a symmetric 99% confidence interval for the population mean playing time of the brand of tape.
b. Does the confidence interval support the customer’s complaints? Give a reason for your answer.
a)
average of sample:
"\\overline{x}=3953.28\/64=61.77"
"z=\\frac{\\overline{x}-\\mu}{\\sigma\/\\sqrt n}"
"\\sigma=\\sqrt{t^2\/(n-1)}=\\sqrt{244557\/63}=62"
critical values for 99% confidence interval:
"z=\\pm 2.576"
"-2.576<\\frac{61.77-\\mu}{62\/\\sqrt{64}}<2.576"
"-19.96<61.77-\\mu<19.96"
"41.81<\\mu<81.73"
b.
The confidence interval support the customer’s complaints, because mean playing time can be less than 60 minutes (minimal value is 41.81 min).
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