Answer:
I. You must use a t test rather than a z-test unless you know the population standard deviation.
Correct when the population deviation is not known we can assume that the distribution follows a t distribution in order to do inferences about the population mean
II. If you do not know the population standard deviation, your sample must be a simple random sample from a normal population.
False is not required since we can use the t distribution when the sample size is not large enough and when the data is not perfectly Normal
III. Sample sizes must be at least 30.
True that ensure that the condition 2) would be satisfied.
Explanation:
In order to make inferences about the population mean we need 4 important conditions:
1) Random: We need data from a random sample of size n out of the population of interest.
2) Normal: We need that the variable follows a Normal distribution. Sometimes we just need that the distribution would be symmetric and with a large sample.
3) Independent: We need that the population would be much larger than the sample (at least 20 or 30 times as large).
4) Standard Deviation: We need to have the population standard deviation.
Now if we analyze one by one the conditons we have:
I. You must use a t test rather than a z-test unless you know the population standard deviation.
Correct when the population deviation is not known we can assume that the distribution follows a t distribution in order to do inferences about the population mean
II. If you do not know the population standard deviation, your sample must be a simple random sample from a normal population.
False is not required since we can use the t distribution when the sample size is not large enough and when the data is not perfectly Normal
III. Sample sizes must be at least 30.
True that ensure that the condition 2) would be satisfied.