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  • https://stats.libretexts.org/Courses/Fresno_City_College/Math_11%3A_Elementary_Statistics/08%3A_Testing_Hypotheses/8.02%3A_Tests_for_a_Population_Mean/8.2.02%3A_Small_Sample_Tests_for_a_Population_Mean
    Previous hypotheses testing for population means was described in the case of large samples. The statistical validity of the tests was insured by the Central Limit Theorem, with essentially no assumpt...Previous hypotheses testing for population means was described in the case of large samples. The statistical validity of the tests was insured by the Central Limit Theorem, with essentially no assumptions on the distribution of the population. When sample sizes are small, as is often the case in practice, the Central Limit Theorem does not apply. One must then impose stricter assumptions on the population to give statistical validity to the test procedure.
  • https://stats.libretexts.org/Courses/Rio_Hondo_College/Math_130%3A_Statistics/08%3A_Hypothesis_Testing_with_One_Sample/8.04%3A_Hypothesis_Testing_of_Single_Mean
    Previous hypotheses testing for population means was described in the case of large samples. The statistical validity of the tests was insured by the Central Limit Theorem, with essentially no assumpt...Previous hypotheses testing for population means was described in the case of large samples. The statistical validity of the tests was insured by the Central Limit Theorem, with essentially no assumptions on the distribution of the population. When sample sizes are small, as is often the case in practice, the Central Limit Theorem does not apply. One must then impose stricter assumptions on the population to give statistical validity to the test procedure.

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