A hospital wants to compare the mean length of stay of its p

A hospital wants to compare the mean length of stay of its patients with the nation-wide (population) mean. Suppose that the nation-wide mean = 3 days, with a standard deviation = 1.5 day. The hospital samples N = 10 of its patients at random and finds that they stayed has mean = 4.3 days. Does mean hospital stay length for patients at this hospital differ from the nation-wide mean? Conduct a statistical test to answer this question. Use α = .05Write down the null and alternative hypotheses using statistical symbols. Explain your symbols________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________What are the critical values? ______________________________________________________________________________What is the test statistic? Show your calculations ____________________________________________________________________________________________________________________________________________________________TURN TO NEXT PAGEWhat is your conclusion? ______________________________________________________________________________Report the results in APA style ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Calculate the 95% confidence interval of mean. What does it mean? Show your calculations ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________A car company claims that their new car model has 31 mpg (miles per gallon) on local traffic. A researcher in Consumer Reports randomly selects 8 of this cars from the local car dealerships and test their gas mileage on local traffic in NYC. The mean mpg is 29, with SD = 2.78. The researcher wants to claim that the actual mean mpg is less than what the company claims. Conduct a statistical test to answer this question. Use α = .01Write down the null and alternative hypotheses using statistical symbols. Explain your symbols________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________What are the critical values? Show your calculations ______________________________________________________________________________What is the test statistic? Show your calculations ____________________________________________________________________________________________________________________________________________________________What is your conclusion? ______________________________________________________________________________Report the results in APA style __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Can the reporter claim that the actual mean mpg is less than what the company claims (31 mpg)? YES or NO? ______________________________________________________________________________