Question

In Major League Baseball, the American League (AL) allows a designated hitter (DH) to bat in place of the pitcher, but in the National League (NL), the pitcher has to bat. However, when an AL team is the visiting team for a game against an NL team, the AL team must abide by the home team’s rules, and thus, the pitcher must bat. A researcher is curious if an AL team would score more runs for games in which the DH was used. She samples 20 games for an AL team for which the DH was used, and 20 games for which there was no DH. The data are below. The population standard deviation for runs scored is known to be 2.49 for both groups. Assume the populations are normally distributed. DH no DH 0 3 8 6 10 2 2 4 3 0 4 5 7 7 8 6 6 1 5 8 1 12 1 4 5 6 4 3 4 4 3 0 8 5 11 2 11 1 0 4 Is there evidence to suggest that more runs are scored in games for which the DH is used? Use α=0.10. Enter the P-Value - round to 4 decimal places. p-value =

Answer 1

Answer :

Given data is :

Sample size for DH = 20

No DH = 20

and standard deviation for DH() and No DH() = 2.49

and table is as follows:

DH ()	No DH ()
0	3
8	6
10	2
2	4
3	0
4	5
7	7
8	6
6	1
5	8
1	12
1	4
5	6
4	3
4	4
3	0
8	5
11	2
11	1
0	4

Null hypothesis is :

Alternative hypothesis is :

where and are denoted as Population mean for DH and No DH.

Now,Test statistics Z = --------------->(1)

where is Sample of DH

i.e =

= (0 + 8 + 10 + 2 + 3 + 4 + 7 + 8 + 6 + 5 + 1 + 1 + 5 + 4 + 4 + 3 + 8 + 11 + 11 + 0) / 20

= 101 / 20

= 5.05

= 5.05

and   =

= (3 + 6 + 2 + 4 + 0 + 5 + 7 + 6 + 1 + 8 + 12 + 4 + 6 + 4 + 3 + 4 + 0 + 5 + 2 + 1 +4) / 20

= 87 / 20

= 4.35

= 4.35

Now substitute the values in equation 1,

Z =

= =

=

=

=

=

=

test statistics Z = 0.8861

From Z value,

using excel "1- [=normsdist(z)]"

P value = 0.3756

P value > 0.10

So,we donot reject null hypothesis

there is no evidence to support the claim that more runs are scored in games for which DH is used