Answer:
The calculated value t = 1.57736 < 1.9845 at 5 % level of significance
Null hypothesis is accepted at 5 % level of significance
There is no significance difference between Design A and Design B
Step-by-step explanation:
Given sample size of design A
n₁ = 50
<em>sample mean of design A x⁻₁ = 4.1 minutes</em>
<em>Sample standard deviation S₁ = 2.2 minutes</em>
Given sample size of design B
n₂ = 50
<em>sample mean of design A x⁻₂ = 3.5 minutes</em>
<em>Sample standard deviation S₂ = 1.5 minutes</em>
<u><em>Null Hypothesis : H₀</em></u> : There is no significance difference between Design A and Design B
<em>Alternative Hypothesis : H₁</em>:There is significance difference between Design A and Design B
Level of significance ∝ = 0.05
Test statistic
where
On calculation , we get
<em>S² = 3.6173</em>
<em>Test statistic </em>
<em> </em><em></em>
<em>On calculation , we get</em>
<em> t = 1.57736</em>
Degrees of freedom
ν = n₁ + n₂ -2 = 50 +50 -2 =98
t₀.₀₂₅ ,₉₈ = 1.9845
<em>The calculated value t = 1.57736 < 1.9845 at 5 % level of significance</em>
<em>null hypothesis is accepted </em>