Customers have been complaining about the weight of 16 oz chips at a grocery store. To investigate, the store randomly sampled 50 bags of chips and found the mean weight $\bar x=$15.07 oz and sample standard deviation was s=0.8 oz. I am a bit confused about whether to use Z or T test statistic. Can I use a Z test since n>30 or is it more appropriate to use T test statistics. Any insight is much appreciated.
2026-03-25 07:45:21.1774424721
Whether to use Z or T test statistic for a sample of 50, known sample variance and unknown population variance
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The p values for either test are so small that it makes little difference in this case. Even if the sample mean were 15.81 oz, no error would be made in rejecting the null at the .05 level even though both are very close to, but less than, .05. While there appears to be no significant difference at n = 50, my reason for not using a Z test is having to remember at which n value there is no significant difference. I don't think there is any danger in committing a Type I or Type II error with this strategy.