Question

ch 20 working with a small sample size, when we replace σ with s in the formula $z=\frac{overline{x}-mu}{sigma/sqrt{n}}$ the distribution of the resulting statistic is: a non - standard normal distribution. a t distribution. the standard normal distribution. question 9 1 pts ch 20* because the t procedures are robust, the most important condition for their safe use is that the population distribution is exactly normal. the data can be regarded as an srs from the population. the population standard deviation σ is known.

Explanation:

For the first question, when dealing with a small sample size and replacing the population standard deviation $\sigma$ with the sample standard deviation $s$ in the formula for the test statistic, the resulting distribution is a $t$ - distribution. This is a fundamental concept in statistical inference for small samples.

For the second question, the robustness of $t$ - procedures means that they are relatively insensitive to departures from normality. However, the most crucial condition for their safe use is that the data can be regarded as a simple random sample (SRS) from the population. This ensures that the sample is representative and that the statistical inferences made are valid.

Answer:

For the first question: a t distribution.
For the second question: the data can be regarded as an SRS from the population.