2. Previous studies claimed that the population mean DailyReadTime among subjects is 145 minutes, with a population standard deviation of 25 minutes. Based on the data, conduct a hypothesis test BY HAND (with a 1% significance level) to see if there is evidence that the population mean DailyReadTime is greater than 145 minutes. a) (1 point ) Write down your null and alternative hypotheses . Be sure to use appropriate notation b) (2 points) Calculate the test statistic BY HAND. Begin by writing down the formula and be sure to use appropriate notation . Round your answer 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 an accurate knowledge of the population standard deviation a) (1 point) Based on the information given, answer the following: (i) How does this problem differ from Problem 2? (ii) Based on this difference, will the test statistic be different? State the name of the test statistic b) Based on the data, conduct a hypothesis test (with a 1% significance level) to see if there is evidence that the population mean DailyReadTime (measured in minutes) is greater than 145 minutes . USE SPSS to find the test statistic and P-value, and as with all work done in SPSS, attach your output . i. (1 point ) Write down your null and alternative hypothesis . Be sure to use appropriate notation