An engineer in charge of water rationing for the U.S. Army wants to determine if the average male soldier spends less time in the shower than the average female soldier. Let He represent the average time in the shower of male soldiers and represent the average time in the shower of female soldiers. a) What are the appropriate hypotheses for the engineer? O Ho: Pm-14 versus Ha: Hm > Hr O Ho: om- of versus Ha: om> or O Ho: Hm- versus Ha: Hm Hr O Ho: Hm 14 versus Ha: Hm < He b) Among a sample of 50 male soldiers the average shower time was found to be 2.66 minutes and the standard deviation was found to be 0.74 minutes. Among a sample of 58 female soldiers the average shower time was found to be 2.81 minutes and the standard deviation was found to be 0.64 minutes. What is the test statistic? Give your answer to three decimal places. [ c) What is the P-value for the test? Give your answer to four decimal places. d) Using a 0.01 level of significance, what is the appropriate conclusion? O Conclude that the average shower time for males is less than the average shower time for females because the P-value is less than 0.1. O Conclude that the average shower time for males is equal to the average shower time for females because the P-value is less than 0.1. O Reject the claim that the average shower times are different for male and female soldiers because the P-value is greater than 0.1. O Fail to reject the claim that the average shower times are the same for male and female soldiers because the P-value is greater than 0.1.