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Sagot :
Answer:
a. Yes
Step-by-step explanation:
The term common variance means that each population has the same variance.
If σ²=σ₁²=σ₂² but unknown then the unbiased pooled or combined estimate of the common variance σ² is calculated.
In the given problem the pooled variance is calculated .
Therefore we assume that that the underlying variances are equal.
Using Student's t distribution
The given data is
Mean 3.74 4.86
Variance 2.78097 0.17142
n 15 15
Pooled variance 1.47620
t= x`1- x`2/ Sp √1/n1+ 1/n2
t = 3.74-4.86/ 1.47620 √1/15+ 1/15
t= -1.12/ 0.539
t= -2.0779
Taking the significance level ∝= 0.05 the
Value of the critical region is t≤ - t∝/2 and t≥ t∝/2 = ±2.048 for
Degrees of freedom = n1+n2- 2= 28
Hence the calculated value of t -2.0779 falls in the critical region therefore null hypothesis is rejected and and it is concluded that the means are not equal.
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