Answer:
Step-by-step explanation:
The objective is to compute that more runs are scored in games for which DH is used
Let 
denote the population mean number of runs scored for DH group
Let 
denote the population mean number of runs scored for DH group
Let 
and 
denote the sample sizes for DH and no DH
From the available information
The population standard deviation of runs score is 2.54 for both the groups.
That is 
The null hypothesis is 
The alternative hypothesis is 
Let the level of significance 
Since, the population standard deviation for both the group is known , even though the sample size is less than 30 , use z test
The test statistic is
The sample mean for the DH group is computed as
The sample mean of no DH is computed as
The test statistic is
P-Value
From the alternative hypothesis, it is clear that the test is one tailed test
P-value = P(Z > z)
1 - normsdist (0.5602)
(using excel function "normsdist(z)")
= 1 - 0.7123
= 0.2877
Therefore, the P-Value is 0.2877
Decision Rule
Reject the null hypothesis , if the p-value is less than the level of significance . that is p-value is < 0.10
Here, the p-value is 0.2877 which is greater than the level of significance 0.10
so , fail to reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that more runs scored in games for which DH is used.
