Question

You wish to test the following claim (H.) at a significance level of a = 0.10. H:41 = 2 H:17 12 You obtain the following two samples of data. Sample #1 80.3 73.8 52.4 51.7 77.5 73.8 62.9 86.7 76.4 42.9 82.6 73.8 55.9 61.6 69.2 70.9 58.4 62 74.2 36.3 66.9 58.4 86.7 31.3 58.3 85.9 73.8 85.9 68.9 66.6 50.3 84.5 70.1 57.9 28.6 70.9 69.3 66.5 57.9 73.7 67.7 76.4 50.3 78.8 76.8 63.3 82 68.9 54.8 91.8 60.7 100.5 62 51 66.6 58.9 71.3 58.9 67.3 80.3 62 59.4 104.9 64.5 62.9 58.9 85.2 77.3 87.5 61.6 74.2 69.7 62.4 54.2 Sample #2 72.1 74.3 46.7 77.5 56.3 68.3 63.7 50.8 60.6 74.9 49.3 48.3 45.5 63.7 77.5 66.1 59.4 59.8 79.1 71.6 49.8 65.3 78.3 71.1 55.5 56.3 62.5 87.2 51.2 73.2 36.3 64.9 31.2 74.2 What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic - What is the p-value for this sample? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to four decimal places.) p-value = 65.470*

Answer 1

For Sample 1 :   

Sample mean using excel function AVERAGE(),    x̅1 =    68.665625

Sample standard deviation using excel function STDEV.S,    s1 =    12.83629797

Sample size,    n1 =    64

For Sample 2 :   

Sample mean using excel function AVERAGE(),    x̅2 =    62.19545455

Sample standard deviation using excel function STDEV.S,    s2 =    14.61362783

Sample size,    n2 =    44

Null and Alternative hypothesis:  

Ho : µ1 = µ2  

H1 : µ1 ≠ µ2  

df = ((s1²/n1 + s2²/n2)²)/[(s1²/n1)²/(n1-1) + (s2²/n2)²/(n2-1) ] = 84.4907 =    84

Test statistic:  

t = (x̅1 - x̅2)/√(s1²/n1 + s2²/n2) = (68.6656 - 62.1955)/√(12.8363²/64 + 14.6136²/44) = 2.374

p-value =T.DIST.2T(2.374, 84) = 0.0199