Suppose we are counting successes in a Poisson process where we expect 15 successes per hour.  What is the variance in the number of successes during a 28 minu

Suppose we are counting successes in a Poisson process where we expect 1/4 of a  success per minute.  What is the standard deviation in the time we must wait to have the first success? Group of answer choices

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 (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. a. Which is the correct null hypothesis? O i. Ho: µ = 300 min O ii: Ho: µ = 270 min %3D O ii. Ho: µ < 300 min iv: Ho: µ < 270 min

Liu et al. (2015) recently reported the results of a study examining whether happy people live longer. The study followed a large sample of British women, aged 50 to 69, over a 10-year period. At the beginning of the study, the women were asked several questions including how often they felt happy. After 10 years, roughly 4% of the women had died. The following table shows a frequency distribution similar to the results obtained in the study. Lived Died Within 10 Years Total Happy Most of the Time 382 18 400 Unhappy Most of the Time 194 6 200 Total 576 24 n = 600 Do the data indicate a significant relationship between living longer and being happy most of the time? Test with α = .05. (Round your answers to two decimal places for χ²-critical and χ².) χ²-critical = χ² = Conclusion: Fail to reject the null hypothesis. There is a relationship between living longer and being happy most of the time. Reject the null hypothesis. There is no relationship between living longer and being…