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
6 6
8 2
2 4
2 0
4 5
7 7
7 6
6 1
5 8
1 12
1 4
5 6
4 3
4 4
2 0
7 5
11 2
10 1
0 4

Required:
a. Is there evidence to suggest that more runs are scored in games for which the DH is used? Use α=0.10.
b. Can it be concluded that more runs are scored in games for which the DH is used?

Step-by-step explanation:

From the given information:

Let:

represent the population mean no. for DH group.

represent the population mean no. for no DH group  

represent the sample sizes of DH

represent the sample sizes of  no DH

Sample size:

For both groups, the population standard deviation of runs scored = 2.54  

i.e

The null & alternative hypothesis;

Level of significance:

The test statistics is:

where;

= sample mean for DH group

= 4.6

= sample mean for no DH group

= 4.15

Now:

= 0.5602

Since the test is one-tailed by looking at that

The P-value =

Using Excel Function " =normdist(z)"; we have":

P-value = 0.2877

Decision rule: To reject , if

Conclusion: SInce P = 0.2877 which is

We fail to reject the and conclude that there is insufficient evidence to support the given claim that:

the naturalist literary movement was an extension of the realist literary movement, a movement that strove to portray life as it really was hope it

step-by-step explanation:

answer: options

step-by-step explanation: