A auto shop wants to examine the proportion of customers that have to return after an appointment. Last year, an examination of 264 customers found that 30.1% had to return after an appointment. You instituted some changes at the auto shop this year, and found from a sample of 326 customers that 22.4% had to return after an appointment. You want to conduct an analysis to determine if there has been an increase in the proportion of customers that need to return after an appointment since the past year, with a 0. 10. Using this information, what is the critical value of your analysis? Round your final answer to two decimal places. = 2.33 1.64 2.11 1.96 1.28

Find the value of x.

Find the value of x

A New York Times article titled For Runners, Soft Ground Can Be Hard on the Body considered two perspectives on whether runners should stick to hard surfaces or soft surfaces following an injury. One position supported running on soft surfaces to relieve joints that were in recovery from injury. The second position supported running on hard surfaces since soft surfaces can be uneven, which may make worse those injuries a soft surface was intended to help. Suppose we are given sufficient funds to run an experiment to study this topic. With no studies to support either position, which of the following hypotheses would be appropriate? The first position is more sensible, so this should be a one-sided test. In this case, we should form the alternative hypothesis around the second position. The second position makes the more sense, so this should be a one-sided test. In this case, we should form the alternative hypothesis around the first position. Because we would be interested in any…