Question

Are there gender differences in the time spent using on social media? A time-tracking software was used to determine the average time on social media websites in a random sample of 31 men and 31 women. Men, on average, spent 49 minutes per day on social media websites, with the standard deviation of 25. Women, on average, spent 52 minutes per day on social media websites, with a standard deviation of 18. Use α=0.05.

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 ╪   0                  
                          
Level of Significance ,    α =    0.05                  
                          
Sample #1   ----> Men   
mean of sample 1,    x̅1=   49.000                  
standard deviation of sample 1,   s1 =    25.000                  
size of sample 1,    n1=   31                  
                          
Sample #2   ----> Women
mean of sample 2,    x̅2=   52.000                  
standard deviation of sample 2,   s2 =    18.000                  
size of sample 2,    n2=   31                  
                          
difference in sample means =    x̅1-x̅2 =    49.0000   -   52.0   =   -3.000  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    21.7830                  
std error , SE =    Sp*√(1/n1+1/n2) =    5.5329                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -3.0000   -   0   ) /    5.53   =   -0.542
                          
Degree of freedom, DF=   n1+n2-2 =    60                  
p-value =        0.5897   (excel function: =T.DIST.2T(t stat,df) )              
Conclusion:     p-value>α , Do not reject null hypothesis                      
                          
There is not enough evidence to conclude that there are gender differences in the time spent using on social media