Question

According to the historical admissions of School of Administrative Studies (ADMS) at York-U, 35% of students chose Accounting as their major, 30% of students specialized in the Finance major, 15% of students registered in the Management stream, 8% of students majored in Marketing area, and the rest of students enrolled in other majors. Currently, the dean is randomly sampling a group of students from School of Administrative Studies (ADMS) and the table below summarizes the students' major specializations by genders. Major Specialization Accounting Finance Management Marketing Other Majors SUMS Male / 36 55 Student 150 Gender 57 20 30 26 Female Student SUMS 150 49 300 Meanwhile, the dean also records the means and standard deviations of 'Grade-Point Average (GPA) for these sampled students from different majors: Major Specialization Finance Management Marketing 6.13 5. 926 .25 1.27 1.34 0.96 GPA Accounting 5.86 1.04 Mean (X) Standard deviation (Si) Other Majors 5.74 1.65 Part I: a) In order to investigate whether the percentage of students who enrolled in the Finance major differs from the historical admissions of School of Administrative Studies, which population parameter and hypothesis test should be used? b) State both hypotheses. c) At 10% of significance level, determine the critical point(s) of rejection region(s). d) Calculate the test-statistic of this hypothesis test. e) Draw the final conclusion of this hypothesis test.

Answer 1

a)

We will use 1 proportion test.

Sample proportion = 75/300 = 0.25

b)

Ho :   p =    0.3                  
H1 :   p ╪   0.3       (Two tail test)          
  

c)

Level of Significance,   α =    0.10                  
Number of Items of Interest,   x =   75                  
Sample Size,   n =    300                  
                          
Sample Proportion ,    p̂ = x/n =    0.2500                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0265                  

                          
critical z value =    ±    1.645   [excel formula =NORMSINV(α/2)]             

d)

Z Test Statistic = ( p̂-p)/SE = (   0.2500   -   0.3   ) /   0.0265   =   -1.8898

e)

  
p-Value   =   0.058781721   [excel formula =2*NORMSDIST(z)]              
Decision:   p-value<α , reject null hypothesis                       
There is enough evidence to prove that percentage of students enrolled in Finance majore differs from historical admission.

Please revert in case of any doubt.

Please upvote. Thanks in advance