Question

A set of data was published in the fall 2019 Phi Kappa Phi Forum regarding the performance of Major League Baseball (MLB) umpires in calling balls and strikes. The article is based on data collected by MLB over eleven seasons (2008-2018). This study shows that it is common for umpires to make incorrect calls more than 20% of the time. An average game has about 300 pitches where the umpire has to make a decision. Assume that we take a random sample of 300 of the 4 million ball/strike calls in the database. From this sample of 300, there were 70 incorrect calls made for a sample proportion of.23. The question is does this one sample of size 300 with 70 incorrect calls provide sufficient evidence to allow us to conclude that the umpires are making bad calls at a rate greater than 20%?
Calculate the value of the Z test statistic using phat - 23 from the above description.

Answer 1

Answer:

The answer is "1.30".

Step-by-step explanation:

Proportion of population$=0.20$

Ratio sample$=\frac{70}{300}=\frac{7}{30}=0.23$

Statistics of the test:

$\to Z=\frac{(0.23-0.2)}{\sqrt{(\frac{0.2\times(1-0.2)}{300})}}$

       $=1.30$