#31). Both pictures are the same problem. 0.01, test the hypothesis that the mean length of stay in a hospital in Australia is more than 3.9Using a =days. Assume that the standard deviation of the lengths of all hospital stays in Australia is known to be 0.71days. Use the p-value method.State the null and alternative hypothesis for this test.Ho:?H: ? vDetermine if this test is left-tailed, right-tailed, or two-tailed.O left-tailedright-tailedO two-tailedShould the standard normal (z) distribution or Student's (t) distribution be used for this test?O The Student's t distribution should be usedO The standard normal (z) 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 Australia is greater than 3.9 days and thus we conclude thatthe average length of stay in a hospital in Australia is likely greater than 3.9 days.O The sample data provide sufficient evidence to reject the null hypothesis that the average length ofstay in a hospital in Australia is 3.9 days and thus we conclude that the average length of stay in ahospital in Australia is likely longer than 3.9 days.O The sample data do not provide sufficient evidence to reject the null hypothesis that the averagelength of stay in a hospital in Australia is 3.9 days and thus we conclude that the average length ofstay in a hospital in Australia is likely 3.9 days.O The sample data provide sufficient evidence to reject the alternative hypothesis that the averagelength of stay in a hospital in Australia is greater than 3.9 days and thus we conclude that theaverage length of stay in a hospital in Australia is likely 3.9 days. According to a study conducted three years ago by the Organisation for Economic Cooperation andDevelopment (OECD), the average length of stay in a hospital was 3.9 days in Australia.A researcher in Australia suspects that the average length of stay in a hospital has actually increased inAustralia since the study was released by the OECD three years ago.To test her suspicion, the researcher selected a random sample of 149 hospital patients in Australia andcalculated the average length of hospital stay. The mean of the sample was found to be 4.1 days.0.01, test the hypothesis that the mean length of stay in a hospital in Australia is more than 3.9Using a =days. Assume that the standard deviation of the lengths of all hospital stays in Australia is known to be 0.71days. Use the p-value method.State the null and alternative hypothesis for this test.Ho: ?H1:? vDetermine if this test is left-tailed, right-tailed, or two-tailed.O left-tailedOright-tailedO two-tailedShould the standard normal (z) distribution or Student's (t) distribution be used for this test?O The Student's t distribution should be usedO The standard normal (z) 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 Australia is greater than 3.9 days and thus we conclude thatthe average length of stay in a hospital in Australia is likely greater than 3.9 days.

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We have given that a study conducted three years ago by the Organisation for Economic Cooperation…