4. Researchers working for a sports drink company W8L blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (H = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? Or is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. c. Which test statistic and sampling distribution under the null should we use?

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4. Researchers working for a sports drink company would like to know if a new
blend if its popular sports drink can help improve marathon runners' final running
time. Marathon times, Y, are known to follow a Normal distribution. Suppose that
runners using the old blend sports drink have a mean finishing time of 300 minutes
(µ = 300 minutes). A random sample of 20 runners was selected to use the new
blend of sports drink in a marathon, finishing with an average time of 270 minutes
and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that
the new blend lowers finishing times? COr is it possible that random chance alone can
explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4-
step procedure. Set your alpha-level to 0.05.
%3D
c. Which test statistic and sampling distribution under the null should we use?
O i. z-score; standard Normal
O ii. t-statistic; Student'st
Transcribed Image Text:4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (µ = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? COr is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. %3D c. Which test statistic and sampling distribution under the null should we use? O i. z-score; standard Normal O ii. t-statistic; Student'st
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