2. Previous studies claim that the population mean VO2 max during moming exercise (VO2Max_Morning) is 47, with 2 population standard deviation of 6.0. Therefore, we have knowledge of the population standard deviation Based on the data, conduct a hypothesis test BY HAND (with a 10% significance level) to see if there is evidence that the population mean VO2Max_Morning is less than 47. 2) (1 point) Write down your mull and alternative hypotheses. Be sure to use appropriate notation b) (2 point:) Calculate the test statistic BY HAND. Begin by writing down the formula and be to use appropriate notation. Round to 2 decimal places and show your work c) (2 points) Give the probability statement for the test statistic and the p-value. Report the p- values to 4 decimal places. d) (2 points) State your conclusion in terms of the story. Make sure to specify whether your conclusion refers to the population or the sample 3. We are still interested in testing the same hypothesis as in problem 2, but we really do not have am accurate knowledge of the population standard deviation 2) (1 point) Based on the information given, anewer the following: (1) How does this problem differ from Problem 2? (mi) Based on this difference, will the test statistic be different? State the name of the teat statistic bj Based on the data, conduct a hypothesis test (with a 506 significance level) to see if there is evidence that the population mean VO2Max_Morning is less than 45. USE SPSS to find the test statictic and P-value, and as with all work done in SPSS, include your output in your Brightspace i. (1 point) State your mall and alternative hypotheses. Be sure to use appropriate notation. fi. (2 points) Give the value of the test statistic (USE SPSS, you should NOT calculate this by hand). lii (2 points) Write down the probability statement and the p-valu: (USE SPSS for the p-value). Round your suswer to 4 decimal places and show your work iv. (1 point) State your conclusion in terms of the story. Make sure to specify whether your conclusion refers to the population or the sample. () (2 points) What is the 95% confidence interval for the population mean VO2Max_Morning? Keep in mind we still don't know the true population standard deviation You should use the SPSS output from (b) and if you are confused, refer to page 11 in the SPSS Instruction Manual. Round your answer to _ decimal places and show your work