1. A fisherman teamed up with a few biologists and statisticians to test the number of fish in the two rivers. They claim that East River has more salmon in it than West River. After some research, they find the following data: East River West River x1=49 salmon x2=45 salmon n1=150 square feet n2=150 square feet Based on historical data, they see that the population standard deviation for East River is 13.4 fish and the population standard deviation for West River is 11.2 fish. The fisherman and his team randomly select locations in each river in which to count the fish. If the rejection region is all z-values greater than z0.025, and the test statistic is z=2.80, what conclusion can be made about the population of salmon in the rivers? 2. Mike, a gas station owner, wanted to know whether the population mean of users paying with credit cards has changed from the years 2005 to 2015. Since Mike has owned the gas station since 2000 he uses historical data and assumes the standard deviation for 2005 is 3.02 and the standard deviation for 2015 is 1.07. Mike selects a random number of transactions in a certain period from both 2005 and 2015. The results of the samples are shown in the table. Assuming the conditions needed for the hypothesis test have been met, what is the z test statistic for this hypothesis test, rounded to two decimal places. 2005 2015 x1=32.1 x2=34.7 n1=148 n2=192 3. An on demand stationary bike company has two bike production facilities. The CEO, John, checks from time to time if the two production facilities are assembling bikes with similar outputs (measured in watts). The two facilities were calibrated at the same time by the company and based on that information the population standard deviation for the first production facility is 0.009 and the population standard deviation for the second production facility is 0.013. John randomly selects bikes produced by the two facilities and the wattage is recorded and shown below. Facility 1 Facility 2 x1=45.3 x2=48.5 n1=209 n2=218 Based on the information above find the null and alternative hypotheses, where 1 is the population mean of facility 1 and 2 is the population mean of facility 2.