When is the z-statistic used to estimate the population mean?a.When the population standard deviation is knownb.When the population standard deviation is unknownc.When the sample size is smalld.When the sample size is large
Question
When is the z-statistic used to estimate the population mean?a.When the population standard deviation is knownb.When the population standard deviation is unknownc.When the sample size is smalld.When the sample size is large
Solution
The z-statistic is used to estimate the population mean in the following situations:
a. When the population standard deviation is known: The z-statistic is used when we have information about the population's standard deviation. This is because the z-statistic formula requires the population standard deviation.
d. When the sample size is large: The z-statistic is also used when the sample size is large (typically n > 30). This is due to the Central Limit Theorem, which states that if the sample size is large enough, the sampling distribution of the mean will be approximately normally distributed, regardless of the shape of the population distribution.
So, the z-statistic is used when the population standard deviation is known and the sample size is large.
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