Question

Use it and Excel to answer this question. It contains Assignment 1 marks for two past sections of this course

Treat it as a random sample. Perform a hypothesis test to determine if the two sample means are equal. Use α = 0.10.

Section A	Section B
15	16
26	52
52	55
53	57.5
54	58
56.5	60
61	61
61.5	70
63	70
66	71
66	72
66.5	73
69	74.5
71	75
77	75.5
77	76
78	77
79	81
81	85
86	85.5
87	86
90	88
90	88.5
91	91
91	93
	94
	95
	96
	98
	98
	99.5
	100

Answer 1

Ho :   µ1 - µ2 =   0              
Ha :   µ1-µ2 ╪   0              
                      
Level of Significance ,    α =    0.1              
                      
Sample #1   ---->   sample 1              
mean of sample 1,    x̅1=   68.30              
standard deviation of sample 1,   s1 =    19.13              
size of sample 1,    n1=   25              
                      
Sample #2   ---->   sample 2              
mean of sample 2,    x̅2=   77.25              
standard deviation of sample 2,   s2 =    18.08              
size of sample 2,    n2=   32              
                      
difference in sample means =    x̅1-x̅2 =    68.3000   -   77.3   =   -8.95
                      
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    N/A              
std error , SE =    Sp*√(1/n1+1/n2) =    4.9846              
                      
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -8.9500   -   0   ) /    4.98   = - 1.796
                      
Degree of freedom, DF=   n1+n2-2 =    50          

   
t-critical value , t* =       1.6759 (excel formula =t.inv(α/2,df)      

   
Decision:   | t-stat | < | critical value |, so, Reject Ho          

conclusion : there is not enough evidence to conclude the   two sample means are equal