Could you please help me express the written in math terms, and also provide charts or graphs to represent?
During the past three (May, June and July) a vast amount of employees been absent from Greg's Grand Corporation. The amount of absences in one department has caused great concern in Greg's Grand Corporation's management team as productivity has decreased significantly. This lead to the idea to test the absences in department Q over the past three months by taking random samples in the company and analyzing the results.
There is a random sample of 25 employees working in department Q at Greg's Grand Corporation who were absent about 15 times on average in the past three months. In regards to The random 25 samples of absentees in department Q, there is a standard deviation of 9 and a level of significance of .05 (a=.05). Does the value of 15 days absent significantly differ from the population value of 12 absent days in Department Q?
The null hypothesis is the high absentee rate of 15 days is the past three months significantly differs form the average days absent in a three month period of 12 days. Mathematically stated the null hypothesis is: Ho: u = 12.
The alternative hypothesis is the high absentee rate of 15 days is the past three months does not significantly differ form the average days absent in a three month period of 12 days. Mathematically stated the alternative null hypothesis is Ho: u does not =12.
The level of significance is a=.05. The level of significance states that there is a 5% margin of error possibility. This gives the opportunity to reject the null hypothesis when the null hypothesis is actually true which leads into a Type I error. Type one error is when the null hypothesis is rejected when the null hypothesis is actually true.
This solution expresses the statements in mathematical terms, and it touches on statistical concepts like decision rule, null hypothesis, and conclusion.