Question

At the beginning of a semester a group of students who were US residents admitted through the regular admissions process and who were taking the same courses were selected based on their high use of social media and the similarities of their college GPA's. The selected students were randomly assigned to one of 2 groups:

At the beginning of a semester a group of students who were US residents admitted through the regular admissions process and who were taking the same courses were selected based on their high use of social media and the similarities of their college GPA'S. The selected students were randomly assigned to one of 2 groups: group 1 students were told to text and use Facebook during classes in their usual high-frequency manner; group 2 students were told to refraln from any use of texting and Facebook during classes. At the condlusion of the semester the semester GPA's of the students were collected. The results are shown in the table below IN-CLASS MUTLITASKING STUDY Frequent Facebook Use and Texting No Facebook Use or Texting X1 2.8/ S 0.67 n 65 X2 3.16 -0.53 n2 65 Do texting and Facebook use during class have a negative affect on GPA? To answer this question perform a hypothesis test with where 11 is he mean semester GPA o a students who lex and use Facebook requently during class and μ21s he mean semester GPA o al students who do no text or use Facebook during class. Question 1. What is the value of the test statistic for this hypothesis test? Qucstion 2. What is the P value for this hypothesis test? Question 3. What is the correct conclusion for this hypothesis test? (1 submission allowed) test statistic P-value (use 4 decimal places) 令Do not reject the null hypothesis; there is no significant difference between the mean GPA of students who frequently text and use Facebook during dass and the mean GPA of students who do not text and use Facebook during class. Reject the null hypothesis and conclude that the mean GPA of students who frequently text and use Facebook during class is less than the mean GPA of students who do not text and use Facebook during class. Reject the null hypothesis and conclude that the mean GPA of students who do not text and use Facebook during class is less than the mean GPA of students who frequently text อnd use Facebook during class. Question 4 Calculate a 95% confidence interval for μ1-2 where μι s the mean semester GPA of all students who text and use Facebook requently during class andH2 s the mean semester GPA of all students who do not text or use Facebook during class. lower limit of confidence interval (use 2 decimal places) upper limit of confidence inter(se 2 decimal places).

Answer 1

    Let μ1 and μ2 be the population means of GPAs of students using facebook and students not using facebook respectively                                                       
   We have to test whether there is a difference between                              
   the GPA scores are negatively affected by texting and facebook usage                              
   Hence                              
   The null and alternative hypothesis are                               
   Ho : μ1 - μ2 = 0 ; HA : μ1 - μ2 < 0                             
                                  
Question 1:                             
   Since sample size is more than 30 , we use the z-test                              
   The test statistic z is calculated as                               
      
n2 (2.87 - 3.16) - (0) (0.67), (0.53% + 65 65
        Here μ1 - μ2 = 0                  
          
                                  
   z = -2.7369                              
   Test Statistic = -2.7369                              
                                  
   Question 2 :                              
   p-value                              
   Since in the alternative hypothesis we test "less than" we use the one-way z-test                              
   We find p-value such that                               
   p-value = P(Z < -2.7369)                              
   We find p-value using z-tables or the Excel function NORM.S.DIST(z, TRUE))                              
   p-value =NORM.S.DIST(-2.7369, TRUE)                              
   p-value = 0.0031          
   p-value = 0.0031                             
                                  
   Question 3 :                             
   Let α = 0.05    Level of significance                          
   0.0031 < 0.05                              
   that is p-value < level of significance                              
   Conclusion :   (Option 2)                          
   Reject the null hypothesis and conclude that the mean GPA of students who frequently                              
   text and use Facebook during class is less than the mean GPA of students who do not                               
   text and use Facebook during class.                             
                                  
   Question 4:                            
   95% confidence interval is given by                               
  
2MSE (x1-x2) ± z- 73
                                          
   where                               
                                  
   Mean Square Error = MSE =
1 , s12+s22
                              
                                  
   MSE =      
(0.67)2+ (0.53)2
                       
                                  
   MSE = 0.3649                              
   95% confidence interval for population mean                              
   For 95%, α = 0.05, α/2 = 0.025                              
   From the z-tables, or Excel function NORM.S.INV(α/2)                              
   z = NORM.S.INV(0.025) = 1.960           (We take the positive value for calculations)                  
   Confidence interval is given by                              

2 0.3649 65 (2.87 3.16) t 1.96
                                                                 
   = -0.29 ± 0.2077                              
   = (-0.4977, -0.0823)                              
(Rounding to two decimals)                                 
   Lower limit of confidence interval = -0.50                              
   Upper limit of confidence interval = -0.08