Question
I'm not asking what is the answer of two questions. I'm wondering when do we use z test and t test. for example is this,
2. The Environmental Protection Agency (EPA) warns communities when their tap water is contaminated with too much lead. Drinking water is only considered safe if the mean concentration of lead is 15 parts per billion or less. The lead concentrations for 16 randomly selected water samples from one community are shown below: 15.2 15.8 12.3 16.7 13.9 14.4 15.0 16.1 14.9 13.3 18.0 15.5 17.6 21.3 10.8 13.6 The sample mean is calculated to be 15.28. Lead concentrations in the community are known to follow a norma distribution wtih standard deviation 2.2 parts per billion. (a) Con struct a 95% confidence interval for the true mean lead concentration of water in the community. (b) Provide an interpretation of the interval in (a), (c ) The EPA would like to conduct a hypothesis test at the 5% level of significance to determine whether there is significant evidence that the tap water in the community is unsafe. Show all of your steps. (d) Provide an interpretation of the P-value of the test in (c). (e) Verify your calculations in the test in (c) using Excel (f) Could the confidence interval in (a) have been used to conduct the test in (c)? Why or why not? If it could be used, what would the conclusion be, and why? If it could not be used, explain why not.
Explanation / Answer
We use Z-test for a large sample, usually sample size >30 and T-test for sample size usually <30.
T-test is used if we do not know the populations’ standard deviation. If populations’ standard deviation is given then it is sure we use z- test at any sample size samll or large.
As for example,
In the 1st numerical, the standard deviation of the population i.e. the whole community is given. So we will use the z-test. But in the 2nd numerical, the standard deviation of the sample i.e. 10 adults is given. So we will use the t-test.
