Answer:
<em>The calculated value Z = 1.8368 < 1.96 at 0.05 level of significance</em>
<em>The null hypothesis is accepted</em>
<em>The samples have been drawn from the same Population</em>
Step-by-step explanation:
<u><em>Step(i):</em></u>-
Given first sample size 'n₁' = 49
Mean of the first sample 'x₁⁻ = 609.86
Standard deviation of the sample S₁ = 55.96 calories
Given first sample size 'n₂' = 78
Mean of the first sample 'x₂⁻ = 641.02
Standard deviation of the sample S₂ = 109.14 calories
<u><em>Step(ii):</em></u>-
<u><em>Null hypothesis </em></u>: H₀: x₁⁻ = x₂⁻
<u><em>Alternative Hypothesis </em></u>: H₁: x₁⁻ ≠ x₂⁻
<em>Level of significance ∝ = 0.05</em>
<em>Test statistic </em>
<em>where </em>
<em> </em>
<em> </em>
<em> σ² = 8660.357</em>
<u><em>Step(iii)</em></u>:-
<em>Test statistic </em>
|Z| = |-1.8368| = 1.8368
<em>The tabulated value Z₀.₉₅ = 1.96</em>
<em>The calculated value = 1.8368 < 1.96 at 0.05 level of significance</em>
<em>The null hypothesis is accepted</em>
<u><em>Final answer</em></u><em>:-</em>
<em>The samples have been drawn from the same Population</em>
<em> </em>