Question

Assume that o1 02 a. Sample 1: 80, 80, 79, 81, 76, 66, 71, 76, 70, 85. Sample 2: 79, 62, 70, 68, 73. 76, 86, 73, 72, 68, 75,
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Answer #1

We find the means and standard deviations for the samples using     
Excel function Average and stdev.s    
we get    

Sample 1 Sample 2
Sample Size n1 = 10 n2 = 12
Sample Mean X̅1 = 76.4 X̅2 = 72.33
Sample Standard Deviation s1 = 5.8348 s2 = 6.3437

Since population standard deviation is not known, we use the t distribution    
Confidence interval is given by     
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For 95%, α = 0.05    
Degrees of freedom = df = n1 + n2 - 2 = 10 + 12 - 2 = 20    
From the t-tables, or Excel function T.INV.2T(α, df)    
t = T.INV.2T(0.05, 20)    
t = 2.086    
95% confidence interval for difference in means is     
(76.4-72.33)± 2.086 (5.8348)- (6.3437) 10 + 12
= 4.07 ± 5.4228    
= (-1.3528, 9.4928)    
    
95% confidence interval for μ1 - μ2 is (-1.3528, 9.4928)    
    

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