EXCEL 

TwoSample Hypothesis ZTest (Variances Known) 











Perform a TwoSample ZTest: 

Assumptions: 

1. Independent Samples. 

2. No assumption about the shape of either population is required. 

3. Variances for both populations are known. 

4. Both samples contain at least 30 observations. 











The following are the grades of 30 students in two sections of a statistics class. 












A 
B 







1 
Section 1 Grade 
Section 2 Grade 







2 
90 
99 







3 
89 
98 







4 
66 
100 







5 
77 
100 







6 
99.9 
99.9 







7 
66 
100 







8 
57 
98 







9 
44 
44 







10 
66 
99 







11 
78 
33 







12 
88 
88 







13 
99 
99 







14 
97 
97 







15 
100 
100 







16 
99 
95 







17 
99 
59 







18 
97 
47.9 







19 
88 
100 







20 
92 
100 







21 
93 
28.2 







22 
54 
98 







23 
68 
86 







24 
84 
56 







25 
91 
28 







26 
76 
97 







27 
73 
55 







28 
87 
76 







29 
92 
89 







30 
94 
51 







31 
38 
43 

















Enter the data; place the grades for section 1 in column A and the grades for section 2 in 



column B. Variances are known to be 25 for each section. 













Compare the grades of the two sections of a statistics class: 

Perform a hypothesis test at the 5% significance level to determine if there exists a 

significant difference in grades of the two sections. 











Perform Hypothesis Test with EXCEL: 



1. Enter the data into columns A and B. 



2. Select Tools and Data Analysis. 



3. Select ZTest: TwoSample for Means and click OK. 



4. Input the following in the dialog box: 



a. Input Variable 1 Range: A1:A31. 


b. Input Variable 2 Range: B1:B31. 


c. Hypothesized Mean Difference: 0. 


d. Input Variable 1 Variance (known): 25 



e. Input Variable 2 Variance (known): 25 



f. Click on Labels (since you included the labels in your input range). 


g. Alpha: 0.05. 


h. Check Output Range and specify the range, if you would like the output on the same 


spreadsheet. Output Range is A35. Choose a New Work Sheet Ply if you like a 


new sheet. 



i. Click OK and you will see the output below. 
















zTest: Two Sample for Means 




















Section 1 Grade 
Section 2 Grade 







Mean 
81.39666667 
78.8 







Known Variance 
25 
25 







Observations 
30 
30 







Hypothesized Mean Difference 
0 








z 
2.011369351 








P(Z<=z) onetail 
0.022143159 








z Critical onetail 
1.644853476 








P(Z<=z) twotail 
0.044286319 








z Critical twotail 
1.959962787 



























Interpret Your Results: 


1. State the hypothesis: 


H_{0}: μ_{1} = μ_{2} 


H_{A}: μ_{1} ≠ μ_{2} 


2. Level of Significance: α = 0.05 and we have a twotailed test. 


3. Determine Test Statistic: z = 2.011 


4. Decision Rule: Critical zValue: Reject Ho if z > 1.96 or z<  1.96. 


5. Make a Decision: Reject Ho since 2.011 does fall into the rejection region. 


6. Conclusion: There exists enough evidence at the 5% significance level to claim that there is 


a significant difference in the grades of the two sections of statistics classes. 
































© copyright 2004 Elisabeth Knowlton