The given statement is false.
Given that,
The z-statistic can be used as the foundation for statistical inferences about the difference in two population means using two independent random samples if the populations are normally distributed but the population variances are unknown.
If the sample sizes are small, the populations are normally distributed, and the population variances are known, the z statistic can be used as the foundation for statistical inferences about the difference between two population means using two independent random samples.
Therefore, the above given statement can be concluded as false.
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