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Answer:
The sample statistics follows a standard normal distribution since the sample size are large enough.
Step-by-step explanation:
Given that:
<u>First population:</u>
Sample size = 49
Population standard deviation = 3
Sample mean = 10
<u>Second population:</u>
Sample size = 64
Population standard deviation = 4
Sample mean = 12
The sample statistics follows a standard normal distribution since the sample size are large enough.
The null and alternative hypotheses can be computed as:
Level of significance = 0.01
Using the Z-test statistics;
Z = - 3.037
Z - 3.04
The P-value = 2P (z < -3.04)
From the z tables
= 2 × (0.00118)
= 0.00236
Thus, since P-value is less than the level of significance, we fail to reject the null hypotheses