Study Session 2 - Hypothesis Testing

[Giles]

Hi everyone
In reading 11 on hypothesis testing (page 595) example 3, question 4 utilizes a z-test even though the sample size (n) is only 24 IE: n≤ 30 and therefore the sample size is small.
Is the z-test used because this question relates to data that is a subset of a large sample of 132? My first instinct was to use the t-test but this is incorrect?
Thanks,

 

[Daniel.V]

When population variance is known, the appropriate is to use Z-test. T-test is more conservative and, unless the distribution is non-normal, can also be used.
If sample < 30 and distribution is non-normal, there’s no appropriate test.

 

[Giles]

Thanks Daniel
What i don’t understand in the context of that question specifically is that the Industrial CP Issues with Inferior Ratings (n=24) is provided with a sample standard error which is derived from sample standard deviation. it does not explicitly state that the population variance is a known quantity.
Part 2 of this example refers to All CPI Issues and is also provided with a sample standard error. If this sample is in fact equal to the whole population (IE: there were only 132 CP issues in total for the period, equivalent to our sample size) and question 4 is a subset of this sample, do we then conclude that population variance is known?