Question

An experiment is conducted to determine if classes offered in an online format are as effective as classes offered in a traditional classroom setting. Students were randomly assigned to one of the two teaching methods. Final exam scores reported below. a. Test the claim that the standard deviations for the two groups are equal. What is the p-value of the test? b. Construct a 95% confidence interval on the difference in expected final exam scores between the two groups. Does the data support the claim that there is no difference? Do not use mini tab

On-line	Classroom
77	79
66	64
70	88
79	80
76	66
58	81
54	71
72	84
56	77
82	76
90	89
68	62
59	74
67	68
71	98
74	77
72	65
62	83
77
78
76
57
67
69
82
78
80
61
77
65
71
76
58
82
78
74

Answer 1

a) let σ1 and σ2 be population std of classroom and online classes.

Ho: σ1 = σ2

H1: σ1 ╪ σ2

class room

Sample Size = 18
Sample Variance,s1² = 94.418

online
Smaller-Variance Sample  
Sample Size = 36
Sample Variance,s2² = 77.1071

F stat = s1²/s2² = 94.418/77.1071 = 1.2245

df1 =n1-1=17

df2=n2-1 = 35

p value =0.5938 [excel fucntion :   =F.DIST.RT(1.2245,17,35) ]

p value >α=0.05,Do not reject the null hypothesis

so, there is not enough evidence to reject the claim

b)

mean of sample 1,    x̅1=   71.0833
standard deviation of sample 1,   s1 =    8.7811
size of sample 1,    n1=   36

      
mean of sample 2,    x̅2=   76.778
standard deviation of sample 2,   s2 =    9.7169
size of sample 2,    n2=   18
      

Degree of freedom, DF=   n1+n2-2 =    52  
t-critical value =    t α/2 =    2.0066   (excel formula =t.inv(α/2,df)

          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    9.0976  
          
std error , SE =    Sp*√(1/n1+1/n2) =    2.6263  
margin of error, E =    t*SE =    5.2700  
          

difference of means =    x̅1-x̅2 =    -5.6944  
confidence interval is           
Interval Lower Limit=   (x̅1-x̅2) - E =    -10.9644  
Interval Upper Limit=   (x̅1-x̅2) + E =    -0.4245  

since, confidence interval do not contain 0, so, data support that there is no difference between two means