According to a study conducted five years ago by the Organisation for Economic Cooperation andDevelopment (OECD), the average length of stay in a hospital was 4.9 days in the United States.A researcher in the United States suspects that the average length of stay in a hospital has actuallyincreased in the United States since the study was released by the OECD five years ago.To test his suspicion, the researcher selected a random sample of 191 hospital patients in the United Statesand calculated the average length of hospital stay. The mean of the sample was found to be 5.06 days.Using a = 0.005, test the hypothesis that the mean length of stay in a hospital in the United States ismore than 4.9 days. Assume that the standard deviation of the lengths of all hospital stays in the UnitedStates is known to be 0.72 days. Use the p-value method.State the null and alternative hypothesis for this test.Ho:?H₁: ? ✓Determine if this test is left-tailed, right-tailed, or two-tailed.two-tailedright-tailedⒸleft-tailedShould the standard normal (2) distribution or Student's (t) distribution be used for this test?The standard normal (2) distribution should be used O The standard normal (z) distribution should be usedThe Student's & distribution should be usedDetermine the test statistic for the hypothesis test. Round the solution to two decimal places.Determine the p-value for the hypothesis test. Round the solution to four decimal places.Determine the appropriate conclusion for this hypothesis test.O The sample data do not provide sufficient evidence to reject the alternative hypothesis that theaverage length of stay in a hospital in the United States is greater than 4.9 days and thus weconclude that the average length of stay in a hospital in the United States is likely greater than 4.9days.O The sample data provide sufficient evidence to reject the alternative hypothesis that the averagelength of stay in a hospital in the United States is greater than 4.9 days and thus we conclude thatthe average length of stay in a hospital in the United States is likely 4.9 days.O The sample data do not provide sufficient evidence to reject the null hypothesis that the averagelength of stay in a hospital in the United States is 4.9 days and thus we conclude that the averagelength of stay in a hospital in the United States is likely 4.9 days.O The sample data provide sufficient evidence to reject the null hypothesis that the average length ofstay in a hospital in the United States is 4.9 days and thus we conclude that the average length ofstay in a hospital in the United States is likely longer than 4.9 days.

Question

Accepted Answer

Given :
μ = 4.9
x¯ = 5.06
σ = 0.72
n = 191
α = 0.005