Question

You want to know whether left handed athletes weigh more or before. You can only find 5 of them. You have have to assum and for this problem you will assume that they are a single random smape from a normal population.

Before	After
175	180
127	120
210	240
195	192
110	112

Test the claim that the weiht of the left hnaded athletes does not chnage from before to after their season. Be sure to give both hypothesis(Ha and Ho), P- value, and a conclusion (reject or fail to reject).

Answer 1

Before                After                       d=Before - After

175                    180                             - 5

127                  120                                7

210                    240                            - 30

195                    192                              3

110                      112                          - 2

Step 1: To find mean difference = :

= - 27/5 = - 5.4
Step 2: To find s_d, SD of difference:

d               d-             (d-)²

- 5               0.4              0.16

7                12.4            153.76

- 30          - 24.6            605.16

3             8.4               70.56

- 2           3.4              11.56

------------------------------------------

Total                          841.2

s²_d = 841.2/4 = 210.3

So,

s_d = 14.5017

Step 3:

H0: = 0

HA: 0

Step 4:

Test statistic is:

t = /SE = - 5.4/6.4853 = - 0.8327

Step 5:

ndf = 5 - 1 = 4

By Technology, P value = 0.4532

Step 6:

Take

= 0.05

Since P - value = 0.4532 is greater than = 0.05, H0 is accepted.

Conclusion:

The claim that the weight of the left handed athlelets does not change from before to after their season is supported by the data.