[求助]某考试统计题

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Researchers wished to know if they could conclude that two populations of infants differ with respect
to mean age at which they walked alone. The following data (ages in months) were collected:
Sample from population A: 9.5, 10.5, 9.0, 9.75, 10.0, 13.0, 10.0, 13.5, 10.0, 9.5, 10.0, 9.75
Sample from population B: 12.5, 9.5, 13.5, 13.75, 12.0, 13.75, 12.5, 9.5, 12.0, 13.5, 12.0, 12.0
What should the researchers conclude? Let a=.05.


这是参加一个考试时候的题，题目中每组sample有12个数据，在Hypothesis Testing的时候应该选择z-statistics还是t-statistics还是t'-statistics，这个我很疑惑，因为考试时候没有提供t-statistics的表，只有z-statistics的表，我只好解释说因为是non-normal distribution，尽管小于30，仍然使用z-statistics去Test。求高人来解答一下，这部分概念不是很明白，谢谢！

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关键词：统计题 distribution Researchers Populations Statistics collected following months should 统计

贴一下我的解答：
Data. The data consist of samples from population A with  x ̅_A=10.3750,  s_A=1.3960 and n_A=12, and samples from population B with  x ̅_B=12.2083,  s_B=1.4493 and n_A=12.

Assumptions. The statistics were computed from two independent samples that behave as simple random samples from two populations of infants.

Hypotheses.
H_0:μ_A-μ_B=0
H_A:μ_A-μ_B≠0

Test statistic. Though the sample size are not large enough, we choose the z-statistics to test the hypothesis. Since the population variances are unknown, we will use the sample variances in the calculation of the test statistic. The test statistic is
z=(〖(x ̅〗_A-x ̅_B)-〖(μ_A-μ_B)〗_0)/√((s_A^2)/n_A +(s_B^2)/n_B )

Distribution of test statistic. If the null hypothesis is true, the test statistic is distributed approximately as the standard normal with μ=0.