Answer:
The calculated value t = 2.366 > 2.0301 at 0.05 level of significance
The null hypothesis is rejected
There is a difference between the means
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given that the first sample size 'n₁' = 22
Given that the mean of the first sample x₁⁻ = 120
Given that the standard deviation of the sample (s₁) = 20
Given that the mean of the second sample x₂⁻ = 100
Given that the standard deviation of the second sample (S₂) = 30
<u><em>Step(ii):-</em></u>
T-test statistic
where
S² = 637.1428
S = √637.1428 = 25.24168
The standard deviation of the sample 'S' = 25.24168
<u><em>Step(iii):-</em></u>
<u><em>Null Hypothesis:H₀:</em></u>
There is no difference between the means
<u><em>Alternative Hypothesis:H₁:</em></u>
There is a difference between the means
T-test statistic
t = 2.366
Degrees of freedom
γ = n₁+n₂ -2 = 22+15-2 = 35
t₀.₀₅ = 2.0301
The calculated value t = 2.366 > 2.0301 at 0.05 level of significance
The null hypothesis is rejected
There is a difference between the means