The director of a research center randomly investigated the weight of 12 adult boys and 12 adult girls (the information is as follows). He has several statistical analyzes he wants to do. Please complete the analyzes assigned by the director.
Note: The weight distribution of adult men and women obeys the norm.
Number 1 2 3 4 5 6 7 8 9 10 11 12
Male 68 68 74 65 72 80 72 81 63 79 75 58
Female 56 61 65 59 64 60 63 71 54 56 65 58
The director wanted to know "whether there is a difference in the weight of adult men and women." It is assumed here that the maternal variation numbers are different, and when performing the test, please use [boy - girl] for calculation. Please answer the following questions respectively:
1.Write down the statistical hypotheses (including null and alternative hypotheses) for the above hypothesis. Please express it mathematically (please pay attention to the use of symbols and subscripts).
2.Write down the statistics (Z, t, chi ^2, F), statistic values, and degrees of freedom for this hypothesis test (if none, please write "none").
3,Is this test a one-tailed or two-tailed test? Please find the critical values required for this test (please write one for a one-tailed test and both for a two-tailed test).
4.Please write down the statistical and textual conclusions of this test