(Confidence intervals and hypothesis testing) The following problems illustrate the common point estimators for constructing intervals and performing hypothesis test (a) Mean of a population of yours, who is the

lead coordinator on Space Mountain, is concerned that the ride is going too fast as it is currently configured. The duration is supposed to average 185seconds per ride over the course of a day, but in a simple random sample of 30 rides over the course of the last 24 hours, the average duration was found to be 182 seconds,with a standard deviation of 2 seconds.You are working as an engineer at Disneyland. A friend (i) Let u denote the true mean duration of rides on Space Mountain, as it is currently configured, in seconds. Construct a 99% confidence interval for µ. Does your confidence interval contain 185 seconds? (ii) Compute the attained significance level for a one-sided hypothesis test with null hypothesis Ho : µ = 185 s and alternative hypothesis Ha : µ< 185 s. (iii) Would the ride be considered to be going too fast at the a = 0.10significance level? What about at the a = 0.05 significance level? (iv) Would you recommend that the ride be reconfigured? Explain.