This paper circulates around the core theme of (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. together with its essential aspects. It has been reviewed and purchased by the majority of students thus, this paper is rated 4.8 out of 5 points by the students. In addition to this, the price of this paper commences from £ 60. To get this paper written from the scratch, order this assignment now. 100% confidential, 100% plagiarism-free.
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!