# (a) (6 marks) Construct and interpret a 99% confidence interval for the population mean reaction time for Shock Jake. Will a 7 second delay be enough? Explain briefly.

01 / 10 / 2021 Statistics

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Question
Radio host Shock Jake encourages listeners to call in to express their views on topical issues.  Radio station YouSayFM has decided to place these calls on a 7 second broadcast delay.  This means Shock Jake can censor a call if inappropriate language is used.

It is believed that reaction times to cut off a caller are Normally distributed.  YouSayFM decided to test Shock Jake’s reaction time, with a sample of 32 trials yielding a mean of exactly 5 seconds and a standard deviation of 2.2 seconds.  YouSaF would like to know whether Shock Jake’s reaction time is fast enough for the proposed broadcast delay.

(a)    (6 marks) Construct and interpret a 99% confidence interval for the population mean reaction time for Shock Jake.  Will a 7 second delay be enough?  Explain briefly.

(b)    (2 marks) Would you advise YouSayFM to reduce the confidence level from 99% to 95% to better determine whether a 7 second delay is enough?  Explain briefly [Hint: consider the impact on the width of the confidence interval when changing confidence level].  Do not perform any calculations.

(c)     (6 marks) Assuming 99% confidence, what is the sample size required to estimate, to within 1 second, the population mean reaction time of Shock Jake.  Have YouSayFM  taken enough samples?

(d)     (6 marks) Radio standards report an average reaction time of 4.5 seconds and a standard deviation of 2.2 seconds. What is the probability that for a sample of 32 reaction times, Shock Jake will produce an average reaction time less than 5 seconds?

Note: If you are using a Normal distribution for this calculation, identify the quantity that follows a Normal distribution and use a diagram!

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