The t distribution should be used when ___.
the sampling population is not normal
the sampling population is unimodal
The sampling distribution is normal and the population standard deviation is unknown
the population standard deviation is known
The sampling distribution is normal and the population standard deviation is unknown
How about the third choice?
The t distribution should be used when the sampling distribution is normal and the population standard deviation is unknown.
The t distribution should be used when the sampling distribution is normal and the population standard deviation is unknown.
To determine which distribution to use, you need to consider two factors: the shape of the sampling distribution and the knowledge of the population standard deviation.
First, consider the shape of the sampling distribution. If the sampling population is not normal or not known to be normal, then you should use the t distribution. The t distribution is more robust than the normal distribution and can handle deviations from normality when the sample size is small.
Second, consider the knowledge of the population standard deviation. If the population standard deviation is known, then you can use the normal distribution. However, if the population standard deviation is unknown, you should use the t distribution. The t distribution takes into account the uncertainty associated with estimating the population standard deviation from the sample data.
Therefore, the t distribution should be used when the sampling population is not normal and when the sampling distribution is normal but the population standard deviation is unknown.