a)
option C
b)
null Hypothesis:μd | = | 0 | |
alternate Hypothesis: μd | < | 0 |
S. No | X | Y | diff:(d)=x1-x2 | d2 |
1 | 52.6 | 55 | -2.4 | 5.76 |
2 | 39.5 | 35.3 | 4.2 | 17.64 |
3 | 71.1 | 78 | -6.9 | 47.61 |
4 | 71.7 | 71.5 | 0.2 | 0.04 |
5 | 74.8 | 83.1 | -8.3 | 68.89 |
6 | 49.8 | 49.2 | 0.6 | 0.36 |
total | = | Σd=-12.6 | Σd2=140.3 | |
mean dbar= | d̅ = | -2.1000 | ||
degree of freedom =n-1 = | 5 | |||
Std deviaiton SD=√(Σd2-(Σd)2/n)/(n-1) = | 5.030000 | |||
std error=Se=SD/√n= | 2.0535 | |||
test statistic = | (d̅-μd)/Se = | -1.02 |
0.05 level with left tail test and n-1= 5 df, critical t= | -2.02 |
fail to reject Ho ; there is not sufficient evidence,,,,,,,,,,,
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