According to a study conducted three years ago by the Organisation for Economic Cooperation and Development OECD the average length of stay in a hospital was 3 6 days in Australia A researcher in Australia suspects that the average length of stay in a hospital has actually increased in Australia since the study was released by the OECD three years ago To test her suspicion the researcher selected a random sample of 165 hospital patients in Australia and calculated the average length of hospital stay The mean of the sample was found to be 3 69 days Using a significance level of 2 test the hypothesis that the mean length of stay in a hospital in Australia is more than 3 6 days Assume that the standard deviation of the lengths of all hospital stays in Australia is known to be 0 46 days Use the p value method State the null and alternative hypothesis for this test Ho V H V Determine if this test is left tailed right tailed or two tailed Otwo tailed Oright tailed Oleft tailed Should the standard normal z distribution or Student s t distribution be used for this test O The standard normal z distribution should be used O The Student s t distribution should be used Determine 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 provide sufficient evidence to reject the alternative hypothesis that the average length of stay in a hospital in Australia is greater than 3 6 days and thus we conclude that the average length of stay in a hospital in Australia is likely 3 6 days The sample data do not provide sufficient evidence to reject the alternative hypothesis that the average length of stay in a hospital in Australia is greater than 3 6 days and thus we conclude that the average length of stay in a hospital in Australia is likely greater than 3 6 days The sample data provide sufficient evidence to reject the null hypothesis that the average length of stay in a hospital in Australia is 3 6 days and thus we conclude that the average length of stay in a hospital in Australia is likely longer than 3 6 days The sample data do not provide sufficient evidence to reject the null hypothesis that the average length of stay in a hospital in Australia is 3 6 days and thus we conclude that the average length of stay in a hospital in Australia is likely 3 6 days