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How do I find the Z score for a statistic without standard deviation given Pop mean equal to $0.05$\%, $n=100$ and sample mean of $0.11$\%?

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Last updated date: 20th Jun 2024
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Answer
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Hint: We first express the process for expressing the Z score for a statistic with standard deviation. For the case when standard deviation is not present, we need a test statistic (t-score) which is dependent on standard error which is dependent on the standard deviation.

Complete step by step solution:
Simply put, a z-score (also called a standard score) gives you an idea of how far from the mean a data point is. Z-scores are a way to compare results to a “normal” population. Results from tests or surveys have thousands of possible results and units; those results can often seem meaningless.
In some cases we can also use two population means instead of using a standard deviation.
The two independent samples are simple random samples from two distinct populations. The test comparing two independent populations with unknown and possibly unequal population standard deviations is called the Aspin-Welch t-test. The degrees of freedom formula were developed by Aspin-Welch.
So, we understand that even for the test statistic (t-score) we need to find the standard error which is dependent on the standard deviation.
Therefore, we can’t find the Z score for a statistic without standard deviation.

Note:
A z-score measures exactly how many standard deviations above or below the mean a data point is. Because we do not know the population standard deviations, we estimate them using the two sample standard deviations from our independent samples.